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Published online by Cambridge University Press:  17 June 2019

Luca Lusanna
Affiliation:
Istituto Nazionale di Fisica Nucleare (INFN), Firenze
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References

Soffel, M.H., Relativity in Astrometry, Celestial Mechanics and Geodesy (Springer, Berlin, 1989).Google Scholar
Kovalevski, J., Mueller, I.I., and Kolaczek, B., Reference Frames in Astronomy and Geophysics (Kluwer, Dordrecht, 1989).Google Scholar
Sovers, O.J. and Fanselow, J.L., Astrometry and Geodesy with Radio Interferometry: Experiments, Models, Results, Rev. Mod. Phys. 70, 1393 (1998).Google Scholar
Wald, R.M., General Relativity (University of Chicago Press, Chicago, 1984 ) .Google Scholar
Ashtekar, A., New Perspectives in Canonical Gravity (Bibliopolis, Naples, 1988).Google Scholar
Ashtekar, A., Lectures on Non-Perturbative Canonical Gravity (World Scientific, Singapore, 1991).Google Scholar
D’Inverno, R., Introducing Einstein Relativity (Oxford University Press, Oxford, 1992).Google Scholar
Christodoulou, D. and Klainerman, S., The Global Nonlinear Stability of the Minkowski Space, (Princeton University Press, Princeton, 1993).Google Scholar
Stewart, J. Advanced General Relativity (Cambridge University Press, Cambridge, 1993).Google Scholar
Ciufolini, I. and Wheeler, J.A., Gravitation and Inertia (Princeton University Press, Princeton, 1995).Google Scholar
Maggiore, M., Gravitational Waves (Oxford University Press, Oxford, 2008).Google Scholar
Gourgoulhon, E., Special Relativity in General Frames (Springer, Berlin, 2013).Google Scholar
Gourgoulhon, E., 3+1 Formalism in General Relativity (Springer, Berlin, 2012).Google Scholar
Straumann, N., General Relativity with Applications to Astrophysics (Springer, Berlin, 2004).Google Scholar
Will, C.M., Theory and Experiment in Gravitational Physics (Cambridge University Press, New York, 1993).Google Scholar
Will, C. M., The Confrontation between General Relativity and Experiment, Living Rev Rel. 9, 1 (2006); 17, 1 (2014) (arXiv 1403.7377)CrossRefGoogle ScholarPubMed
Will, C. M., Was Einstein Right? A Centenary Assessment (2014) (arXiv 1409.7871).Google Scholar
Rovelli, C., Quantum Gravity (Cambridge University Press, Cambridge, 2004).Google Scholar
Thiemann, T., Modern Canonical Quantum General Relativity (Cambridge University Press, Cambridge, 2007).Google Scholar
Dirac, P.A.M., Lectures on Quantum Mechanics (Yeshiva University, New York, 1964);Google Scholar
Dirac, P. A. M., Generalized Hamiltonian Dynamics, Can. J. Math. 2, 129 (1950).CrossRefGoogle Scholar
Anderson, J.L. and Bergmann, P. G., Constraints in Covariant Field Theories, Phys. Rev. 83, 1018 (1951).Google Scholar
Bergmann, P.G. and Goldberg, J., Dirac Bracket Transformations in Phase Space, Phys. Rev. 98, 531 (1955).CrossRefGoogle Scholar
Bergmann, P.G., Observables in General Relativity, Rev. Mod. Phys. 33, 510 (1961).Google Scholar
Hanson, A.J., Regge, T., and Teitelboim, C., Constrained Hamiltonian Systems, in Contributi del Centro Linceo Interdisciplinare di Scienze Matematiche, et al. (Accademia Nazionale dei Lincei, Roma, 1975).Google Scholar
Henneaux, M. and Teitelboim, C., Quantization of Gauge Systems (Princeton University Press, Princeton, 1992).Google Scholar
Sundermeyer, K., Constraint Dynamics with Applications to Yang-Mills Theory, General Relativity, Classical Spin, Dual String Model (Springer, Berlin, 1982).Google Scholar
Gitman, D.M. and Tyutin, I.V., Quantization of Fields with Constraints (Springer, Berlin, 1990).Google Scholar
Govaerts, J., Hamiltonian Quantization and Constrained Dynamics (Leuwen University Press, Leuwen, 1991).Google Scholar
Lusanna, L., Dirac–Bergmann Constraints in Physics: Singular Lagrangians, Hamiltonian Constraints and the Second Noether Theorem, Int. J. Geom. Meth. Mod. Phys. 15, 18300 04 (2018) (arXiv 1702.07598).Google Scholar
Guinot, B., Applications of General Relativity to Metrology, Metrologia 42, 261 (2005).Google Scholar
Soffel, M., Klioner, S.A., Petit, G., et al., The IAU 2000 Resolutions for Astrometry, Celestial Mechanics and Metrology in the Relativistic Framework: Explanatory Supplement, Astron. J. 126, 2687, (2003) (arXiv astro-ph/0303376).Google Scholar
McCarthy, D.D. and Petit, G., IERS Conventions (2003) (Verlag des BKG, Frankfurt am Main, 2004)Google Scholar
Kaplan, G.H., The IAU Resolutions on Astronomical Reference Systems, Time Scales and Earth Rotation Models, U.S. Naval Observatory Circular No. 179 (2005) (arXiv astro-ph/0602086).Google Scholar
Moyer, T.D., Formulation for Observed and Computed Values of Deep Space Network Data Types for Navigation (John Wiley, New York, 2003).Google Scholar
Lusanna, L., Relativistic Metrology: From Earth to Astrophysics, in Modern Metrology Concerns, ed. Cocco, L. (InTech, London, 2012)Google Scholar
Lusanna, L. and Stanga, R., Relativistic Celestial Metrology: Dark Matter as an Inertial Gauge Effect, in Trends in Modern Cosmology, ed. Capistrano de Souza, A.J. (Intech, Rijeka, 2017) (arXiv 1502.06801).Google Scholar
Villani, M., Constraints on ADM Tetrad Gravity Parameter Space from S2 Star in the Center of the Galaxy and from the Solar System, 2015 (arXiv:1502.06801).Google Scholar
Pauri, M. and Prosperi, G. M., Canonical Realizations of the Rotation Group, J. Math. Phys. 8, 2256 (1967)Google Scholar
Pauri, M. and Prosperi, G. M., Canonical Realizations of the Galilei Group, J. Math. Phys. 9, 1146 (1968)Google Scholar
Pauri, M. and Prosperi, G. M., Canonical Realizations of the Poincare Group: 1. General Theory, J. Math. Phys. 16, 1503 (1975)Google Scholar
Pauri, M. and Prosperi, G. M., Canonical Realization of the Poincare Group I. Space-Time Description of Two Particles Interacting at a Distance, Newtonian-Like Equations of Motion and Approximately Relativistic Lagrangian Formulation, J. Math. Phys. 17, 1468 (1976).Google Scholar
Pauri, M., Canonical Realizations of the Poincare Group with Increasing Mass-Spin Trajectories, in Group Theoretical Methods in Physics, ed. K. B. Wolf (Springer, Berlin, 1980).Google Scholar
Littlejohn, R. G. and Reinsch, M., Gauge Fields in the Separation of Rotations and Internal Motions in the N-Body Problem, Rev. Mod. Phys. 69, 213 (1997).Google Scholar
Alba, D., Lusanna, L., and Pauri, M., Dynamical Body Frames, Orientation–Shape Variables and Canonical Spin Bases for the Nonrelativistic N-Body Problem, J. Math. Phys. 43, 373 (2002).Google Scholar
DePietri, R., Lusanna, L., and Pauri, M., Gauging Kinematical and Internal Symmetry Groups for Extended Systems: The Galilean One-Time and Two-Times Harmonic Oscillators, Class. Quantum Grav. 11, 1417 (1996).Google Scholar
Alba, D., Lusanna, L., and Pauri, M., Multipolar Expansions for Closed and Open Systems of Relativistic Particles, J. Math. Phys. 46(2005).Google Scholar
Longhi, G., Lusanna, L., and Pons, J.M., On the Many-Time Formulation of Classical Particle Mechanics, J. Math. Phys., 1893 30(1989).Google Scholar
De Pietri, R., Lusanna, L., and Pauri, M., Standard and Generalized Newtonian Gravities as ‘Gauge’ Theories of the Extended Galilei Group: I. The Standard Theory. Class. Quantum Grav. 12, 219 (1995).Google Scholar
De Pietri, R., Lusanna, L., and Pauri, M., Standard and Generalized Newtonian Gravities as ‘Gauge’ Theories of the Extended Galilei Group: II. Dynamical 3-Spaces Theories, Class. Quantum Grav. 12, 255 (1995).Google Scholar
Alba, D., Quantum Mechanics in Noninertial Frames with a Multitemporal Quantization Scheme: II. Nonrelativistic Particles, Int. J. Mod. Phys. A21, 3917 (2006) (arXiv hep-th/0504060).Google Scholar
Perlick, V., Characterization of Standard Clocks by Means of Light Rays and Freely Falling Particles, Gen. Rel. Grav. 19, 1059 (1987)Google Scholar
Perlick, V., Characterization of Standard Clocks in General Relativity, in Semantic Aspects of Space-Time Theories, eds. Majer, U. and Schimdt, H.J. (Bl-Wissenschaftsverlag, Mannheim, 1994).Google Scholar
Ehlers, J., Pirani, F.A.E., and Schild, A., The Geometry of Free-Fall and Light Propagation in General Relativity, in Papers in Honor of J.L. Synge, ed. O’Raifeartaigh, L. (Oxford University Press, London, 1972).Google Scholar
Mashhoon, B., The Hypothesis of Locality and Its Limitations, in Relativity in Rotating Frames, eds. Rizzi, G. and Ruggiero, M. L. (Kluwer, Dordrecht, 2003) (arXiv gr-qc/0303029).Google Scholar
Mashhoon, B., Limitations of Spacetime Measurements, Phys. Lett. A143, 176 (1990).Google Scholar
Mashhoon, B., The Hypothesis of Locality in Relativistic Physics, Phys. Lett. A145, 147 (1990).Google Scholar
Mashhoon, B., Measurement Theory and General Relativity, in Black Holes: Theory and Observation, eds. Hehl, F. W., Kiefer, C., and Metzler, R. J. K. (Springer, Heidelberg, 1998).Google Scholar
Mashhoon, B., Acceleration-Induced Nonlocality, in Advances in General Relativity and Cosmology, ed. Ferrarese, G. (Pitagora, Bologna, 2003) (arXiv grqc/0301065).Google Scholar
Mashhoon, B. and Muench, U., Length Measurement in Accelerated Systems, Ann. Phys. (Leipzig) 11, 532 (2002).Google Scholar
Alba, D. and Lusanna, L., Simultaneity, Radar 4-Coordinates and the 3+1 Point of View about Accelerated Observers in Special Relativity (2003) (arXiv grqc/0311058)Google Scholar
Alba, D. and Lusanna, L., Generalized Radar 4-Coordinates and Equal-Time Cauchy Surfaces for Arbitrary Accelerated Observers, Int. J. Mod. Phys. D16, 1149 (2007) (arXiv gr-qc/0501090).Google Scholar
Boersma, S. and Dray, T., Slicing, Threading and Parametric Manifolds, Gen. Rel. Grav. 27, 319 (1995) (arXiv gr-qc/9407020).Google Scholar
Jantzen, R. J., Carini, P., and Bini, D., The Many Faces of Gravito-Magnetism, Ann. Phys. (N.Y.) 215, 1 (1992) (arXiv gr-qc/0106043).Google Scholar
Jantzen, R.J., Carini, P., and Bini, D., Relative Observer Kinematics in General Relativity, Class. Quantum Grav. 12, 2549 (1995).Google Scholar
Jantzen, R.J., Carini, P., and Bini, D., The Intrinsic Derivatives and Centrifugal Forces in General Relativity: 1. Theoretical Foundations, Int. J. Mod. Phys. D6, 1 (1997) (arXiv gr-qc/0106013).Google Scholar
Jantzen, R.J., Carini, P., and Bini, D., The Intrinsic Derivatives and Centrifugal Forces in General Relativity: 2. Applications to Circular Orbits in Some Familiar Stationary Axisymmetric Space-Times, Int. J. Mod. Phys. D6, 143 (1997) (arXiv gr-qc/0106014).Google Scholar
Jantzen, R.J., Carini, P., and Bini, D., The Inertial Forces: Test Particle Motion Game, 1998 (arXiv gr-qc/9710051).Google Scholar
Bini, D., Merloni, A., and Jantzen, R. T., Adapted Frames for Space-Time Splittings with an Additional Observer Family, Nuovo Cimento 113B, 611 (1998).Google Scholar
Bini, D. and Jantzen, R. T., Circular Holonomy, Clock Effects and Gravito-Magnetism: Still Going Around in Circles after All These Years, in Proceedings of the 9th ICRA Workshop on Fermi and Astrophysics, 2001, eds. Ruffini, R. and Sigismondi, C. (World Scientific, Singapore, 2002) (arXiv gr-qc/0202085).Google Scholar
Sachs, R.K. and Wu, H., General Relativity for Mathematicians (Springer, Berlin, 1977).Google Scholar
Fermi, E., Sopra i Fenomeni che Avvengono in Vicinanza di una Linea Oraria, Atti Acad. Naz. Lincei Rend. Cl. Sci. Fiz. Mat. Nat. 31, 184, 306 (1922).Google Scholar
Manasse, F.K. and Misner, C.W., Fermi Normal Coordinates and Some Basic Concepts in Differential Geometry, J. Math. Phys. 4, 735 (1963).CrossRefGoogle Scholar
Ni, W.T. and Zimmermann, M., Inertial and Gravitational Effects in the Proper Reference Frame of an Accelerated, Rotating Observer, Phys. Rev. D17, 1473 (1978).Google Scholar
Marzlin, K.P., On the Physical Meaning of Fermi Coordinates, Gen. Rel. Grav. 26, 619 (1994).Google Scholar
Marzlin, K.P., What is the Reference Frame of an Accelerated Observer?, Phys. Lett. A215, 1 (1996).Google Scholar
Marzke, R.F. and Wheeler, J.A., Gravitation as Geometry: I. The Geometry of the Space-Time and the Geometrodynamical Standard Meter, in Gravitation and Relativity, eds. Chiu, H.Y. and Hoffman, W.F. (Benjamin, New York, 1964).Google Scholar
Misner, C.W., Thorne, K.S. and Wheeler, J.A., Gravitation (Freeman, New York, 1973).Google Scholar
Pauri, M. and Vallisneri, M., Marzke–Wheeler Coordinates for Accelerated Observers in Special Relativity, Found. Phys. Lett. 13, 401 (2000) (arXiv grqc/0006095).Google Scholar
Rizzi, G. and Ruggiero, M.L., eds., Relativity in Rotating Frames: Relativistic Physics in Rotating Reference Frames (Kluwer, Dordrecht, 2003).Google Scholar
Rizzi, G. and Tartaglia, A., Speed of Light on Rotating Platforms, Found. Phys. 28, 1663 (1998) (arXiv gr-qc/9805089).Google Scholar
Rizzi, G. and Tartaglia, A., On Local and Global Measurements of the Speed of Light on Rotating Platforms, Found. Phys. Lett. 12, 179 (1999).Google Scholar
Stedman, G.E., Ring-Laser Tests of Fundamental Physics and Geophysics, Rep. Prog. Phys. 60, 615 (1997).Google Scholar
Post, E.J., Sagnac Effect, Rev. Mod. Phys. 39, 475 (1967).CrossRefGoogle Scholar
Derrick, G.H., Classical Mechanics with Respect to an Observer’s Past Light Cone, J. Math. Phys. 38, 64 (1987).Google Scholar
Havas, P., Simultaneity, Conventionalism, General Covariance and the Special Theory of Relativity, Gen. Rel. Grav. 19, 435 (1987).Google Scholar
Møller, C.M., The Theory of Relativity (Oxford University Press, Oxford, 1957)Google Scholar
Møller, C.M., Sur la Dinamique des Syste’mes ayant un Moment Angulaire Interne, Ann. Inst. H. Poincaré 11, 251 (1949).Google Scholar
Dirac, P.A.M., Forms of Relativistic Dynamics, Rev. Mod. Phys. 21, 392 (1949).Google Scholar
Crater, H.W. and Lusanna, L., Non-Inertial Frames in Minkowski Space-Time, Accelerated either Mathematical or Dynamical Observers and Comments on Non-Inertial Relativistic Quantum Mechanics, Int. J. Geom. Met. Mod. Phys. 11, 1450086 (2014) (arXiv 1405.3257).Google Scholar
Bondi, H., Assumption and Myth in Physical Theory (Cambridge University Press, Cambridge, 1967).Google Scholar
Bini, D., Lusanna, L. and Mashhon, B., Limitations of Radar Coordinates, Int.J.Mod.Phys. D14, 1 (2005) (arXiv gr-qc/0409052).Google Scholar
Lusanna, L., Classical Yang-Mills Theory with Fermions: I. General Properties of a System with Constraints, Int. J. Mod. Phys. A10, 3531 (1995).Google Scholar
Lusanna, L., Classical Yang-Mills Theory with Fermions: II. Dirac’s Observables, Int. J. Mod. Phys. A10, 3675 (1995).Google Scholar
Alba, D. and Lusanna, L., The Einstein-Maxwell-Particle System in the York Canonical Basis of ADM Tetrad Gravity: I. The Equations of Motion in Arbitrary Schwinger Time Gauges, Canad. J. Phys. 90, 1017 (2012) (arXiv 4087.0907).Google Scholar
Alba, D. and Lusanna, L., The Einstein-Maxwell-Particle System in the York Canonical Basis of ADM Tetrad Gravity: II. The Weak Field Approximation in the 3-Orthogonal Gauges and Hamiltonian Post-Minkowskian Gravity -the N-Body Problem and Gravitational Waves with Asymptotic Background, Canad.J. Phys. 90, 1077 (2012) (arXiv 1003.5143).Google Scholar
Alba, D. and Lusanna, L., The Einstein-Maxwell-Particle System in the York Canonical Basis of ADM Tetrad Gravity: III. The Post-Minkowskian N-Body Problem, its Post-Newtonian Limit in Non-Harmonic 3-Orthogonal Gauges and Dark Matter as an Inertial Effect, Canad. J. Phys. 90, 1131 (2012) (arXiv 1009.1794).Google Scholar
Alba, D. and Lusanna, L., Charged Particles and the Electro-Magnetic Field in Non-Inertial Frames: I. Admissible 3+1 Splittings of Minkowski Spacetime and the Non-Inertial Rest Frames, Int. J. Geom. Methods Mod. Phys. 7, 33 (2010) (arXiv 0908.0213).Google Scholar
Alba, D. and Lusanna, L., Charged Particles and the Electro-Magnetic Field in Non-Inertial Frames: II. Applications: Rotating Frames, Sagnac Effect, Faraday Rotation, Wrap-up Effect, Int. J. Geom. Methods Mod. Phys. 7, 185 (2010) (arXiv 0908.0215).Google Scholar
Alba, D., Crater, H.W., and Lusanna, L., Towards Relativistic Atom Physics: I. The Rest-Frame Instant Form of Dynamics and a Canonical Transformation for a System of Charged Particles plus the Electro-Magnetic Field, Canad. J. Phys. 88, 379 (2010) (arXiv 0806.2383).Google Scholar
Alba, D., Crater, H.W., and Lusanna, L., Towards Relativistic Atom Physics: II. Collective and Relative Relativistic Variables for a System of Charged Particles plus the Electro-Magnetic Field, Canad. J. Phys. 88, 425 (2010) (arXiv 0811.0715).Google Scholar
Stergioulas, N., Rotating Stars in Relativity, Living Rev. Relativ. 6, 3 (2003).Google Scholar
Alba, D. and Lusanna, L., Quantum Mechanics in Noninertial Frames with a Multitemporal Quantization Scheme: I. Relativistic Particles, Int. J. Mod. Phys. A21, 2781 (2006) (arXiv hep-th/0502194).Google Scholar
Alba, D. and Lusanna, L., Dust in the York Canonical Basis of ADM Tetrad Gravity: The Problem of Vorticity, Int. J. Geom. Meth. Mod. Phys. 12, 1550076 (2015) (arXiv 1106.0403).Google Scholar
Lusanna, L., The N- and 1-Time Classical Descriptions of N-Body Relativistic Kinematics and the Electromagnetic Interaction, Int. J. Mod. Phys. A12, 645 (1997).Google Scholar
Schmutzer, E. and Plebanski, J., Quantum Mechanics in Noninertial Frames of Reference, Fortschr. Phys. 25, 37 (1978).Google Scholar
Lusanna, L. and Materassi, M., A Canonical Decomposition in Collective and Relative Variables of a Klein–Gordon Field in the Rest-Frame Wigner-Covariant Instant Form, Int. J. Mod. Phys. A15, 2821 (2000) (arXiv hep-th/9904202).Google Scholar
Bigazzi, F. and Lusanna, L., Dirac Fields on Spacelike Hypersurfaces, Their Rest-Frame Description and Dirac Observables, Int. J. Mod. Phys. A14, 1877 (1999) (arXiv hep-th/9807054).Google Scholar
Weinberg, S., The Theory of Fields, 3 volumes (Cambridge University Press, Cambridge, 1995, 1996, and 2000).Google Scholar
Thomas, L.H., The Relativistic Dynamics of a System of Particles Interacting at a Distance, Phys. Rev. 85, 868 (1952).Google Scholar
Bakamjian, B. and Thomas, L.H., Relativistic Particle Dynamics II, Phys. Rev. 92, 1300 (1953).Google Scholar
Foldy, L.L., Relativistic Particle Systems with Interactions, Phys. Rev. 122, 275 (1961).Google Scholar
Foldy, L.L., Relativistic Particle Systems, Phys. Rev. D15, 3044 (1977).Google Scholar
Bel, L., Dynamique des Systmes de N Particules Ponctuelles en Relativit Restreinte, Ann. Inst. Henri Poincaré A12, 307 (1970).Google Scholar
Bel, L., Predictive Relativistic Mechanics, Ann. Inst. Henri Poincaré A14, 189 (1971). Hamiltonian Poincaré Invariant Systems, Ann. Inst. Henri Poincaré 18, 57 (1973).Google Scholar
Bel, L. and Martin, J., Formes Hamiltoniennes et Systemes Conservatifs, Ann. Inst. Henri Poincaré 22, 173 (1975).Google Scholar
Bel, L. and Fustero, X., Mcanique Relativiste Predictive des Systmes de N Particules, Ann. Inst. Henri Poincaré 25, 411 (1976).Google Scholar
Currie, D.G., Poincaré-Invariant Equations of Motion for Classical Particles, Phys. Rev. 142, 817 (1966).Google Scholar
Hill, R.N., Canonical Formulation of Relativistic Mechanics, J. Math. Phys. 8, 201 (1967).Google Scholar
Currie, D.G., Jordan, T.F., and Sudarshan, E.C.G., Relativistic Invariance and Hamiltonian Theories of Interacting Particles, Rev. Mod. Phys. 35, 350 (1965).Google Scholar
Leutwyler, H., A No-Interaction Theorem in Classical Relativistic Hamiltonian Particle Mechanics, Nuovo Cimento 37, 556 (1965).Google Scholar
Chelkowski, S., Nietendel, J., and Suchanek, R., The No-Interaction Theorem in Relativistic Particle Mechanics, Acta Phys. Pol. B11(1980) 809.Google Scholar
Sudarshan, E.C.G. and Mukunda, N., Classical Mechanics: A Modern Perspective (Wiley, New York 1974).Google Scholar
Droz Vincent, Ph., Hamiltonian Systems of Relativistic Particles, Rept. Math. Phys. 8, 79 (1975).CrossRefGoogle Scholar
Droz Vincent, Ph., Two-Body Relativistic Systems, Ann. Inst. H. Poincare Phys. Theor. 27, 407 (1977).Google Scholar
Droz Vincent, Ph., N Body Relativistic Systems, Ann. Inst.H. Poincare Phys. Theor. 32, 377 (1980).Google Scholar
Droz Vincent, Ph., Two-Body Relativistic Scattering of Directly Interacting Particles, Phys. Rev. D29, 687 (1984).Google Scholar
Droz Vincent, Ph., Hamiltonian Two-Body System in Special Relativity, Int. J. Theor. Phys. 50, 3481 (2011).Google Scholar
Todorov, I.T., On the Quantification of a Mechanical System with Second Class Constraints, Ann. Inst. Henri Poincaré 28A, 207 (1978).Google Scholar
Todorov, I.T., Constraint Hamiltonian Approach to Relativistic Point Particle Dynamics, SISSA report, 1980.Google Scholar
Todorov, I.T., Constraint Hamiltonian Dynamics of Directly Interacting Relativistic Point Particle, in Quantum Theory, Groups, Fields and Particles, ed. Barut, A.O. (Reidel, Dordrecht, 1983).Google Scholar
Rizov, V.A., Sazdjian, H., and Todorov, I.T., On the Relativistic Quantum Mechanics of Two Interacting Spinless Particles, Ann. Phys. (N.Y.) 165, 59 (1985).Google Scholar
Komar, A., Constraint Formalism of Classical Mechanics, Phys. Rev. D18, 1881 (1978).Google Scholar
Komar, A., Interacting Relativistic Particles, Phys. Rev. D18, 1887 (1978).Google Scholar
Komar, A., Space-Time Orbits for Interacting Relativistic Particles: Syntactic Versus Semantic Observables, Phys. Rev. D18, 3617 (1978).Google Scholar
Komar, A., Constraints, Hermiticity and Correspondence, Phys. Rev. D19, 2908 (1979).Google Scholar
Lusanna, L., A Model for N Classical Relativistic Particles, sNuovo Cimento 65B, 135 (1981).Google Scholar
Lusanna, L., From Relativistic Mechanics towards Green’s Functions: Multi-Temporal Dynamics, in Proc. of the VII Seminar on Problems of High Energy Physics and Quantum Field Theory, Protvino USSR 1984, vol. I.Google Scholar
Longhi, G. and Lusanna, L., Bound-State Solutions, Invariant Scalar Products, and Conserved Currents for a Class of Two-Body Relativistic Systems, Phys. Rev. D34, 3707 (1986).Google Scholar
Alba, D., Crater, H.W., and Lusanna, L., Relativistic Quantum Mechanics and Relativistic Entanglement in the Rest-Frame Instant Form of Dynamics, J. Math. Phys. 52, 062301 (2011) (arXiv 0907.1816).Google Scholar
Alba, D., Crater, H.W., and Lusanna, L., Hamiltonian Relativistic Two-Body Problem: Center of Mass and Orbit Reconstruction, J. Phys. A40, 9585 (2007) (arXiv gr-qc/0610200).Google Scholar
Alba, D., Lusanna, L., and Pauri, M., Centers of Mass and Rotational Kinematics for the Relativistic N-Body Problem in the Rest-Frame Instant Form, J. Math. Phys. 43, 1677 (2002) (arXiv hep-th/0102087).Google Scholar
Lusanna, L., The Chrono-Geometrical Structure of Special and General Relativity: A Re-Visitation of Canonical Geometrodynamics, Lectures at 42nd Karpacz Winter School of Theoretical Physics: Current Mathematical Topics in Gravitation and Cosmology, Ladek, Poland, 6-11 February 2006, Int. J. Geom. Meth. Mod. Phys. 4, 79 (2007) (arXiv gr-qc/0604120).Google Scholar
Lusanna, L., The Chronogeometrical Structure of Special and General Relativity: Towards a Background-Independent Description of the Gravitational Field and Elementary Particles, in General Relativity Research Trends, ed. Reiner, A. (Nova Science, New York, 2005) (arXiv gr-qc/0404122).Google Scholar
Lusanna, L., From Clock Synchronization to Dark Matter as a Relativistic Inertial Effect, Lecture at the Black Objects in Supergravity School BOSS2011, Frascati, 9-13 May 2011, Springer Proc. Phys. 144, 267 (2013) (arXiv 1205.2481).Google Scholar
Lusanna, L., Non-Inertial Frames in Special and General Relativity, in Gravity: Where do We Stand?, eds. Peron, R., Colpi, M., Gorini, V., and Moschella, U. (Springer, Berlin, 2016) (arXiv 1310.4465).Google Scholar
Veneziano, G., Quantum Strings and the Constants of Nature, in The Challenging Questions, ed. Zichichi, A. (Plenum Press, New York, 1990).Google Scholar
Epstein, H., Glaser, V., and Jaffe, A., Nonpositivity of the Energy Density in Quantized Field Theories, Nuovo Cimento 36, 1016 (1965).Google Scholar
Crater, H.W. and Lusanna, L., The Rest-Frame Darwin Potential from the Lienard-Wiechert Solution in the Radiation Gauge, Ann. Phys. (N.Y.) 289, 87 (2001).Google Scholar
Alba, D., Crater, H.W., and Lusanna, L., The Semiclassical Relativistic Darwin Potential for Spinning Particles in the Rest Frame Instant Form: Two-Body Bound States with Spin 1/2 Constituents, Int. J. Mod. Phys. A16, 3365 (2001) (arXiv hep-th/0103109).Google Scholar
Alba, D. and Lusanna, L., The Lienard–Wiechert Potential of Charged Scalar Particles and their Relation to Scalar Electrodynamics in the Rest-Frame Instant Form, Int. J. Mod. Phys. A13, 2791 (1998) (arXiv hep-th/0708156).Google Scholar
Dixon, W.G., Extended Objects in General Relativity: Their Description and Motion, in Isolated Gravitating Systems in General Relativity, Proceedings of the International School of Physics, Enrico Fermi LXVII, ed. Ehlers, J. (North-Holland, Amsterdam, 1979).Google Scholar
Dixon, W.G., Mathisson’s New Mechanics: Its Aims and Realisation, Acta Physica Polonica B Proc. Suppl. 1, 27 (2008)Google Scholar
Dixon, W.G., Description of Extended Bodies by Multipole Moments in Special Relativity, J. Math. Phys. 8, 1591 (1967).Google Scholar
Alba, D., Lusanna, L., and Pauri, M., New Directions in Non-Relativistic and Relativistic Rotational and Multipole Kinematics for N-Body and Continuous Systems, in Atomic and Molecular Clusters: New Research, ed. Ping, Y.L. (Nova Science, New York, 2006) (arXiv hep-th/0505005).Google Scholar
Hegerfeldt, G.C., Remark on Causality and Particle Localization, Phys. Rev. D10, 3320 (1974).Google Scholar
Hegerfeldt, G.C., Violation of Causality in Relativistic Quantum Theory?, Phys. Rev. Lett. 54, 2395 (1985).Google Scholar
Fleming, D.G.N., Covariant Position Operators, Spin and Locality, Phys. Rev. 137B, 188 (1965).Google Scholar
Fleming, D.G.N., Non-Local Properties of Stable Particles, Phys. Rev. 139B, 963 (1965).Google Scholar
Fleming, D.G.N., A Manifestly Covariant Description of Arbitrary Dynamical Variables in Relativistic Quantum Theory, J. Math. Phys. 7, 1959 (1966).CrossRefGoogle Scholar
Fleming, G.N. and Bennet, H., Hyperplane Dependence in Relativistic Quantum Mechanics, Found. Phys. 19, 231 (1989).Google Scholar
Butterfield, J. and Fleming, G., Strange Positions, in From Physics to Philosophy, eds. J. Butterfield and C. Pagonis (Cambridge University Press, Cambridge, 1999).Google Scholar
Zurek, W.H., Decoherence, Einselection and the Quantum Origins of the Classical, Rev. Mod. Phys. 75, 715 (2003).Google Scholar
Einstein, A., Podolski, B., and Rosen, N., Can Quantum-Mechanical Description of Physical Reality be Considered Complete?, Phys. Rev. 47, 777 (1935).Google Scholar
Brown, H.R., Physical Relativity: Space-Time Structure from a Dynamical Perspective (Oxford University Press, Oxford, 2005).Google Scholar
Lusanna, L. and Pauri, M., On the Transition from the Quantum to the Classical Regime for Massive Scalar Particles: A Spaziotemporal Approach, Eur. Phys. J. Plus 129, 178 (2014) (arXiv 1207.1248).Google Scholar
Crater, H.W. and Lusanna, L., On Relativistic Entanglement and Localization of Particles and on their Comparison with the Nonrelativistic Theory, Int. J. Mod. Phys. A29, 1450163 (2014) (arXiv 1306.6524).Google Scholar
Crater, H.W. and Lusanna, L., Non-Inertial Frames in Minkowski Space-Time, Accelerated Either Mathematical or Dynamical Observers and Comments on Non-Inertial Relativistic Quantum Mechanics, Int. J. Geom. Met. Mod. Phys. 11, 1450086 (2014) (arXiv 1405.3257).Google Scholar
Lusanna, L., Classical Observables of Gauge Theories from the Multitemporal Approach, Contemp. Math. 132, 531 (1992)Google Scholar
Lusanna, L., From Relativistic Mechanics towards Green’s Functions: Multitemporal Dynamics, Proceedings of the VII Seminar on Problems of High Energy Physics and Quantum Field Theory, Protvino 1984 (Protvino University Press, Protvino, 1984).Google Scholar
Bigazzi, F. and Lusanna, L., Spinning Particles on Spacelike Hypersurfaces and their Rest-Frame Description, Int. J. Mod. Phys. A14, 1429 (1999).Google Scholar
Lucenti, A., Lusanna, L. and Pauri, M., Dirac Observables and Spin Bases for n Relativistic Spining Particles, J. Phys. A31, 1633 (1998).Google Scholar
Bini, D. and Lusanna, L., Spin-Rotation Couplings: Spinning Test Particles and Dirac Fields, Gen. Rel. Grav. 40, 1145 (2008) (arXiv 0710.0791).Google Scholar
Berezin, F.A. and Marinov, M.S., Classical Spin and Grassmann Algebra, JEPT Lett. 21, 375 (1975).Google Scholar
Barducci, A. and Lusanna, L., The Photon in Pseudoclassical Mechanics, Nuovo Cimento 77A, 39 (1983).Google Scholar
Alba, D., Crater, H.W., and Lusanna, L., Massless Particles Plus Matter in the Rest-Frame Instant Form of Dynamics, J. Phys. A43, 405203 (2010) (arXiv 1005.5521).Google Scholar
Alba, D., Crater, H.W., and Lusanna, L., A Relativistic Version of the Two-Level Atom in the Rest-Frame Instant Form of Dynamics, J. Phys. A46, 195303 (2013) (arXiv 1107.1669).Google Scholar
Alba, D., Crater, H.W., and Lusanna, L., The Rest-Frame Instant Form and Dirac Observables for the Open Nambu String, Eur. Phys. J. Plus 126, 26 (2011) (arXiv 1005.3659).Google Scholar
Colomo, F., Longhi, G. and Lusanna, L., Classical Solutions of the Many-Time Functional Equations of Motion of the Nambu String, Int. J. Mod. Phys. A5, 3347 (1990).Google Scholar
Colomo, F., Longhi, G., and Lusanna, L., Classical Canonical Observables of the Nambu String, Mod. Phys. Lett. A5, 17 (1990).Google Scholar
Colomo, F. and Lusanna, L., Wigner Theory of the Nambu String: I. The Open String, Int. J. Mod. Phys. A7, 1705 (1992).Google Scholar
Colomo, F. and Lusanna, L., Wigner Theory of the Nambu String: II. The Closed String, Int. J. Mod. Phys. A7, 4107 (1992).Google Scholar
Lusanna, L. and Valtancoli, P., Dirac’s Observables for the Higgs Model: I. The Abelian Case, Int. J. Mod. Phys. A12, 4769 (1997).Google Scholar
Lusanna, L. and Valtancoli, P., Dirac’s Observables for the Higgs Model: II. The Non-Abelian SU(2) Case, Int. J. Mod. Phys. A12, 4797 (1997).Google Scholar
Alba, D. and Lusanna, L., The Classical Relativistic Quark Model in the Rest-Frame Wigner-Covariant Coulomb Gauge, Int. J. Mod. Phys. A13, 3275 (1998) (arXiv hep-th/9705156).Google Scholar
Lusanna, L. and Valtancoli, P., Dirac’s Observables for the SU(3) ⊗SU(2)⊗U(1) Standard Model, Int. J. Mod. Phys. A13, 4605 (1998).Google Scholar
Longhi, G. and Materassi, M., A Canonical Decomposition in Collective and Relative Variables of a KleinGordon Field in the Rest-Frame Wigner-Covariant Instant Form, Int. J. Mod. Phys. A14, 3387 (1999) (arXiv hep-th/9809024).Google Scholar
Longhi, G. and Materassi, M., A Canonical Realization of the BMS Algebra, J. Math. Phys. 40, 480 (1999) (arXiv hep-th/9803128).Google Scholar
Dirac, P.A.M., Gauge Invariant Formulation of Quantum Electrodynamics, Can. J. Phys. 33, 650 (1955).Google Scholar
Cohen-Tannoudji, C., Dupont-Roc, J. and Grynberg, G., Atom–Photon Interactions: Basic Processes and Applications (Wiley, New York, 1992).Google Scholar
Cohen-Tannoudji, C., Dupont-Roc, J., and Grynberg, G., Photons and Atoms: Introduction to Quantum Electrodynamics (Wiley, New York, 1989).Google Scholar
Rohrlich, F., Classical Charged Particles (Addison-Wesley, Reading, MA, 1965).Google Scholar
Parrot, S., Relativistic Electrodynamics and Differential Geometry (Springer, New York, 1987).Google Scholar
Poisson, E., An Introduction to the Lorentz-Dirac Equation (arXiv grqc/9912045).Google Scholar
Feynman, R.P. and Wheeler, J.A., Interaction with the Absorber as the Mechanism of Radiation, Rev. Mod. Phys. 17, 157 (1945).Google Scholar
Feynman, R.P. and Wheeler, J.A., Classical Electrodynamics in Terms of Direct Interparticle Action, Rev. Mod. Phys. 21, 425 (1949).Google Scholar
Berezin, F.A., The Method of Second Quantization (Academic Press, New York, 1966).Google Scholar
Itzykson, C. and Zuber, J.B., Quantum Field Theory (McGraw-Hill, Singapore,1987 ).Google Scholar
O’Raifeartaigh, L., Group Structure of Gauge Theories (Cambridge University Press, Cambridge, 1986).Google Scholar
Wilcox, R.M., Exponential Operators and Parameter Differentiation in Quantum Physics, J. Math. Phys. 8, 962 (1967).Google Scholar
Chakrabarti, A., Relativistic Position Operator for Free Particles, J. Math. Phys. 4, 1223 (1963).Google Scholar
Arms, J.M., Marsden, J.E., and Moncrief, V., Symmetry and Bifurcations of Momentum Mappings, Commun. Math. Phys. 78, 455 (1981).Google Scholar
Arms, J.M., Symmetry and Solution Set Singularities in Hamiltonian Field Theories, Acta Phys. Pol. B17, 499 (1986).Google Scholar
Gribov, V.N., Quantization of Nonabelian Gauge Theories, Nucl. Phys. B139, 1 (1978).Google Scholar
Moncrief, V., Gribov Degeneracies: Coulomb Gauge Conditions and Initial Value Constraints, J. Math. Phys. 20, 579 (1979).Google Scholar
Canfora, F., deMicheli, F., Salgado-Robelledo, P., and Zanelli, J., Gribov Ambiguity and Degenerate Systems, Phys. Rev. D90, 044065 (2014) (arXiv 1405.0394).Google Scholar
Vandersickel, N. and Zwanziger, D., The Gribov Problem and QCD Dynamics, Phys. Report 520, 175 (2012) (arXiv 1202.1491).Google Scholar
Kobayashi, S. and Nomizu, K., Foundations of Differential Geometry (Inter-science, New York, 1963).Google Scholar
Trautman, A., Differential Geometry for Physicists (Bibliopolis, Napoli, 1984).Google Scholar
Schmidt, R., Infinite Dimensional Hamiltonian Systems (Bibliopolis, Napoli, 1987).Google Scholar
Abraham, R., Marsden, J.E., and Ratiu, T., Manifolds, Tensor Analysis and Applications (Springer, Berlin, 1988).Google Scholar
Binz, E., Śniatycki, J., and Fischer, H., Geometry of Classical Fields (North-Holland, Amsterdam, 1988).Google Scholar
Lusanna, L. and Nowak-Szczepaniak, D., The Rest-Frame Instant Form of Relativistic Perfect Fluids with Equation of State ρ = ρ(η, s) and of Nondissipative Elastic Materials. Int. J. Mod. Phys. 15, 4943 (2000).Google Scholar
Alba, D. and Lusanna, L., Generalized Eulerian Coordinates for Relativistic Fluids: Hamiltonian Rest-Frame Instant Form, Relative Variables, Rotational Kinematics. Int. J. Mod. Phys. 19, 3025 (2004) (arXiv hep-th/0209032).Google Scholar
Alba, D., Crater, H.W., and Lusanna, L., On the Relativistic Micro-Canonical Ensemble and Relativistic Kinetic Theory for N Relativistic Particles in Inertial and Non-Inertial Rest Frames. Int. J. Geom. Methods Mod. Phys. 12, 1550049 (2015) (arXiv 1202.4667 version 2).Google Scholar
Alba, D., Crater, H.W., and Lusanna, L., On the Relativistic Micro-Canonical Ensemble and Relativistic Kinetic Theory for N Relativistic Particles in Inertial and Non-Inertial Rest Frames. Int. J. Geom. Methods Mod. Phys. 12, 1550049 (2015) (arXiv 1202.4667 version 1)Google Scholar
Lusanna, L., From Relativistic Mechanics towards Relativistic Statistical Mechanics, Entropy 19, 436 (2017).Google Scholar
Brown, J.D., Action Functionals for Relativistic Perfect Fluids, Class. Quantum Grav. 10, 1579 (1993).Google Scholar
Israel, W., Covariant Fluid Mechanics and Thermodynamics: An Introduction, in Relativistic Fluid Dynamics, eds. A. Anile and Y. Choquet-Bruhat (Springer, Berlin, 1989).Google Scholar
Lin, C.C., Hydro-dynamics of Helium II, in Liquid Helium, ed. Careri, G. (Academic Press, New York, 1963).Google Scholar
Serrin, J., Mathematical Principles of Classical Fluid Mechanics, in Handbuch der Physik vol. 8, eds. Flügge, S. and Truesdell, C. (Springer, Berlin, 1959).Google Scholar
Kijowski, J. and Tulczyjew, W.M., A Symplectic Framework for Field Theories, (Springer, Berlin, 1979).Google Scholar
Kijowski, J. and Tulczyjew, W.M., Relativistic Hydrodynamics of Isentropic Flows, Mem. Acad. Sci. Torino V 6, 3 (1982).Google Scholar
Künzle, H.P. and Nester, J.M., Hamiltonian Formulation of Gravitating Perfect Fluids and the Newtonian Limit, J. Math. Phys. 25, 1009 (1984).Google Scholar
Kijowski, J. and Magli, G., Unconstrained Hamiltonian Formulation of General Relativity with Thermo-Elastic Sources, Class. Quantum Grav. 15, 3891 (1998).Google Scholar
Adler, S. and Buchert, T., Lagrangian Theory of Structure Formation in Pressure-Supported Cosmological Fluids, Astron. Astrophys. 343, 317 (1999) (arXiv astroph/9806320).Google Scholar
Bao, D., Marsden, J., and Walton, R., The Hamiltonian Structure of General Relativistic Perfect Fluids, Commun. Math. Phys. 99, 319 (1985).Google Scholar
Holm, D.D., Hamiltonian Techniques for Relativistic Fluid Dynamics and Stability Theory, in Relativistic Fluid Dynamics, eds. Anile, A. and Choquet-Bruhat, Y. (Springer, Berlin, 1989).Google Scholar
Huang, K., Statistical Mechanics (Wiley, New York, 1987).Google Scholar
De Groot, S.R., van Leeuwen, W.A., van Weert, C.G., Relativistic Kinetic Theory: Principles and Applications (North-Holland, Amsterdam, 1980).Google Scholar
Steward, J.M., Non-Equilibrium Relativistic Kinetic Theory (Springer, Berlin/Heidelberg, 1971).Google Scholar
Balescu, R., Relativistic Statistical Thermodynamics, Physica 40, 309 (1968).Google Scholar
Liboff, R.L., Kinetic Theory: Classical, Quantum and Relativistic Descriptions, 2nd ed. (Wiley, New York, 1998).Google Scholar
Hakim, R., Introduction to Relativistic Statistical Mechanics: Classical and Quantum (World Scientific, Singapore, 2011)Google Scholar
Hakim, R., Remarks on Relativistic Statistical Mechanics I, J. Math. Phys. 8, 1315 (1967).Google Scholar
Hakim, R. and Mangeney, A., Relativistic Kinetic Equations Includin Radiation Effects, I: Vlasov Approximation, J. Math. Phys. 9, 116 (1968).Google Scholar
Lehmann, E., Covariant Equilibrium Statistical Mechanics, J. Math. Phys. 47, 023303 (2006).Google Scholar
Horwitz, L.P., Schieve, W.C., Piron, C., Gibbs Ensembles in Relativistic Classical and Quantum Mechanics, Ann. Phys. 137, 306 (1981).Google Scholar
Horwitz, L.P., Shashoua, S., Schieve, W.C., A Manifestly Covariant Relativistic Boltzmann Equation for the Evolution of a System of Events. Physica 161, 300 (1989).Google Scholar
Ares de Parga, G. and López-Carrera, B., Relativistic Statistical Mechanics vs. Relativistic Thermodynamics, Entropy 13, 1664 (2011).Google Scholar
Rickayzen, G., and Powles, J. G., Temperature in the Classical Microcanonical Ensemble, J. Chem. Phys. 114, 4333 (2001).Google Scholar
Rugh, H.H., Dynamical Approach to Temperature, Phys. Rev. Lett. 78, 772 (1997).Google Scholar
Rugh, H.H., A Geometric, Dynamical Approach to Thermodynamics, J. Phys. 31, 7761 (1998) (arXiv chao-dyn/9703013).Google Scholar
Andersen, J.U., Bonderup, E., Hansen, K., On the Concept of Temperature for a Small Isolated System, J. Chem. Phys. 114, 6518 (2001).Google Scholar
Belega, E.D., Cheremukhin, E.A., Elyutin, P.V., and Trubnikov, D.N., On the Definition of the Microcanonical Temperature of Small Weakly Bound Molecular Clusters, Chem. Phys. Lett. 496, 167 (2010).Google Scholar
Giardiná, C. and Livi, R., Ergodic Properties of Microcanonical Observables, J. Stat. Phys. 91, 1027 (1998).Google Scholar
Votyakov, E.V., Hidmi, H.T., DeMartino, A. and Gross, D.H.E., Microcanonical Mean-Field Thermodynamics of Self-Gravitating and Rotating Systems, Phys. Rev. Lett. 89, 031101 (2002).Google Scholar
Becattini, F. and Ferroni, L., The Microcanonical Ensemble of the Ideal Relativistic Quantum Gas with Angular Momentum Conservation, Eur. Phys. J. 52, 597 (2007).Google Scholar
Campa, A., Dauxois, T., and Ruffo, S., Statistical Mechanics and Dynamics of Solvable Models with Long-Range Interactions, Phys. Rep. 480, 57 (2009) (arXiv 0907.0323).Google Scholar
Campa, A., Dauxois, T., Fanelli, D., and Ruffo, S., Physics of Long-Range Interacting Systems (Oxford University Press, London, 2014).Google Scholar
Rocha Filho, T.M., Amato, M.A., and Figueiredo, A., A Novel Approach to the Determination of Equilibrium Properties of Classical Hamiltonian Systems with Long-Range Interactions, J. Phys. 42, 165001 (2009).Google Scholar
Touchette, H., The Large Deviation Approach to Statistical Mechanics, Phys. Rep. 478, 1 (2009).Google Scholar
Van Kampen, N.G., Relativistic Thermodynamics of Moving Systems, Phys. Rev. 173, 295 (1968).Google Scholar
Bíró, T.S. and Ván, P., About the Temperature of Moving Bodies, Europhys. Lett. 89, 30001 (2010).Google Scholar
Mi, D., Zhong, H.Y., Tong, D.M., The Existing Different Proposals for Relativistic Temperature Transformations: The Whys and Wherefores, Mod. Phys. Lett. 24, 73 (2009).Google Scholar
Wu, Z.C., Inverse Temperature 4-Vector in Special Relativity, Europhys. Lett. 88, 20005 (2009).Google Scholar
Sewell, G.I., Note on the Relativistic Thermodynamics of Moving Bodies, J. Phys. 43, 485001 (2010) (arXiv 1010.2045).Google Scholar
Yuen, C.K., Lorentz Transformations of Thermodynamic Quantities, Am. J. Phys. 38, 246 (1970).Google Scholar
Nakamura, T.K., Three Views of a Secret in Relativistic Thermodynamics, Prog. Theor. Phys. 128, 463 (2012) (arXiv 0812.3725).Google Scholar
De Parga, G.A. and López-Carrera, B., Redefined Relativistic Thermodynamics based on the Nakamura Formalism, Physica 388, 4345 (2009).Google Scholar
Hilbert, S., Hänggi, P., Dunkel, J., Thermodynamical Laws in Isolated Systems, Phys. Rev. 90, 062116 (2014).Google Scholar
Poisson, E., The Motion of Point Particles in Curved Spacetime, Living Rev. Relativ. 7, 6 (2004) (arXiv gr-qc/0306052).Google Scholar
Tuckerman, M., The Ideal Gas: Microcanonical Ensemble Treatment, Lectures in Statistical Mechanics (2003). Available online: www.nyu.edu/classes/tuckerman/stat.mech/lectures/lecture-6/node2.htlm.Google Scholar
Bergmann, P., Generalized Statistical Mechanics, Phys. Rev. 84, 1026 (1951).Google Scholar
Matolcsi, T., Kristóf, J., Székely, M., On the Momentum Distribution of Molecules of an Ideal Gas, Publ. Appl. Anal. 7, 1 (1996).Google Scholar
Boisseau, B. and Van Leeuwen, W.A., Relativistic Boltzmann Theory in D+1 Spacetime Dimensions, Ann. Phys. 195, 376 (1989).Google Scholar
Cercignani, C. and Kreimer, G.M., The Relativistic Boltzmann Equation: Theory and Applications (Birkhäuser, Basel, 2002).Google Scholar
Strain, R.M., Global Newtonian Limit for the Relativistic Boltzmann Equation near Vacuum, SIAM J. Math. Anal. 42, 1568 (2010).Google Scholar
Strain, R.M., Coordinates in the Relativistic Boltzmann Theory, Kinet. Relat. Model. 4, 345 (2011) (arXiv 1011.5093).Google Scholar
Norton, J., General Covariance and the Foundations of General Relativity: Eight Decades of Dispute, Rep. Prog. Phys. 56, 791 (1993).Google Scholar
Lusanna, L. and Pauri, M., Explaining Leibniz Equivalence as Difference of Non-inertial Appearances: Dis-solution of the Hole Argument and Physical Individuation of Point-Events, Hist. Philos. Mod. Phys. 37, 692 (2006) (arXiv gr-qc/0604087).Google Scholar
Lusanna, L. and Pauri, M., The Physical Role of Gravitational and Gauge Degrees of Freedom in General Relativity. I: Dynamical Synchronization and Generalized Inertial Effects, Gen. Rel. Grav. 38, 187 (2006) (arXiv gr-qc/0403081).Google Scholar
Lusanna, L. and Pauri, M., The Physical Role of Gravitational and Gauge Degrees of Freedom in General Relativity. II: Dirac versus Bergmann Observables and the Objectivity of Space-Time, Gen. Rel. Grav. 38, 229 (2006) (arXiv grqc/0407007).Google Scholar
Lusanna, L. and Pauri, M., Dynamical Emergence of Instantaneous 3-Spaces in a Class of Models of General Relativity, in Relativity and the Dimensionality of the World, ed. van der Merwe, A. (Springer, Berlin, 2007) (arXiv gr-qc/0611045).Google Scholar
Cacciapuoti, L. and Salomon, C., ACES: Mission Concept and Scientific Objective, ESA document (Estec, March 28, 2007).Google Scholar
Blanchet, L., Salomon, C., Teyssandier, P., and Wolf, P., Relativistic Theory for Time and Frequency Transfer to Order 1/c3, Astron. Astrophys. 370, 320 (2000).Google Scholar
Lusanna, L., Dynamical Emergence of 3-Space in General Relativity: Implications for the ACES Mission, in Proceedings of the 42th Rencontres de Moriond Gravitational Waves and Experimental Gravity, La Thuile (Italy), March 11–18, 2007.Google Scholar
Arnowitt, R., Deser, S. and Misner, C.W., Canonical Variables for General Relativity, Phys. Rev. 117, 1595 (1960)Google Scholar
Arnowitt, R., Deser, S., and Misner, C.W., The Dynamics of General Relativity, in Gravitation: An Introduction to Current Research, ed. Witten, L. (Wiley, New York, 1962) (arXiv gr-qc/0405109).Google Scholar
Lusanna, L., The Rest-Frame Instant Form of Metric Gravity. Gen. Rel. Grav. 33, 1579, (2001) (arXiv gr-qc/0101048).Google Scholar
Lusanna, L. and Russo, S., A New Parametrization for Tetrad Gravity, Gen. Rel. Grav. 34, 189 (2002) (arXiv gr-qc/0102074).Google Scholar
De Pietri, R., Lusanna, L., Martucci, L. and Russo, S., Dirac’s Observables for the Rest-Frame Instant Form of Tetrad Gravity in a Completely Fixed 3-Orthogonal Gauge, Gen. Rel. Grav. 34, 877 (2002) (arXiv gr-qc/0105084).Google Scholar
Agresti, J., De Pietri, R., Lusanna, L., and Martucci, L., Hamiltonian Linearization of the Rest-Frame Instant Form of Tetrad Gravity in a Completely Fixed 3-Orthogonal Gauge: A Radiation Gauge for Background-Independent Gravitational Waves in a Post-Minkowskian Einstein Spacetime, Gen. Rel. Grav. 36, 1055 (2004) (arXiv gr-qc/0302084).Google Scholar
Alba, D. and Lusanna, L., The York Map as a Shanmugadhasan Canonical Transformation in Tetrad Gravity and the Role of Non-Inertial Frames in the Geometrical View of the Gravitational Field, Gen. Rel. Grav. 39, 2149 (2007) (arXiv gr-qc/0604086 v2).Google Scholar
Lusanna, L. and Villani, M., Hamiltonian Expression of Curvature Tensors in the York Canonical Basis: I) Riemann Tensor and Ricci Scalars, Int. J. Geom. Meth. Mod. Phys. 11, 1450052 (2014) (arXiv 1401.1370).Google Scholar
Lusanna, L. and Villani, M., Hamiltonian Expression of Curvature Tensors in the York Canonical Basis: II) Weyl Tensor, Weyl Scalars, Weyl Eigenvalues and the Problem of the Observables of the Gravitational Field, Int. J. Geom. Meth. Mod. Phys. 11, 1450053 (2014) (arXiv 1401.1375).Google Scholar
Lusanna, L., Killing Symmetries as Hamiltonian Constraints, Int. J. Geom. Meth. Mod. Phys. 13, 1650044 (2016) (arXiv 1108.3224).Google Scholar
Lusanna, L., Canonical ADM Tetrad Gravity: From Metrological Inertial Gauge Variables to Dynamical Tidal Dirac Observables, Int. J. Geom. Meth. Mod. Phys. 12, 1530001 (2015) (arXiv 1401.1375).Google Scholar
Isham, C.J. and Kuchar, K., Representations of Spacetime Diffeomorphisms: I. Canonical Parametrized Field Theories, Ann. Phys. (N.Y.) 164, 288 (1984).Google Scholar
Isham, C.J. and Kuchar, K., Representations of Spacetime Diffeomorphisms: II. Canonical Geometrodynamics, Ann. Phys. (N.Y.) 164, 316 (1984).Google Scholar
Kuchar, K., Canonical Geometrodynamics and General Covariance, Found. Phys. 16, 193 (1986).Google Scholar
Nakahara, M., Geometry, Topology and Physics (IOP, Bristol, 1990).Google Scholar
O’Neil, B., Semi-Riemannian Geometry (Academic Press, New York, 1983).Google Scholar
Regge, T. and Teitelboim, C., Role of Surface Integrals in the Hamiltonian Formulation of General Relativity, Ann. Phys. (N.Y.) 88, 286 (1974).Google Scholar
Beig, R. and Ó. Murchadha, , The Poincaré Group as the Symmetry Group of Canonical General Relativity, Ann. Phys. (N.Y.) 174, 463 (1987).Google Scholar
Andersson, L., Momenta and Reduction for General Relativity, J. Geom. Phys. 4, 289 (1987).Google Scholar
Thiemann, T., Generalized Boundary Conditions for General Relativity for the Asymptotically Flat Case in Terms of Ashtekar’s Variables, Class. Quantum Grav. 12, 181 (1995).Google Scholar
Ashtekar, A., Asymptotic Structure of the Gravitational Field at Spatial Infinity, in General Relativity and Gravitation, vol. 2, ed. Held, A. (Plenum, New York, 1980).Google Scholar
Ashtekar, A. and Hansen, R.O., A Unified Treatment of Null and Spatial Infinity in General Relativity: I. Universal Structure, Asymptotic Symmetries, and Conserved Quantities at Spatial Infinity, J. Math. Phys. 19, 1542 (1978).Google Scholar
Ashtekar, A. and Magnon, A., From io to the 3+1 Description of Spatial Infinity, J. Math. Phys. 25, 2682 (1984).Google Scholar
Ashtekar, A. and Romano, J.D., Spatial Infinity as a Boundary of Spacetime, Class. Quantum Grav. 9, 1069 (1992).Google Scholar
Geroch, R., Spinor Structure of Space-Times in General Relativity I, J. Math. Phys. 9, 1739 (1968).Google Scholar
Bleecker, D., Gauge Theory and Variational Principles (Addison-Wesley, London, 1981).Google Scholar
Sen, A., Quantum Theory of Spin-3/2 Field in Einstein Spaces, Int. J. Theor. Phys. 21, 1 (1982).Google Scholar
Sommers, P., Space Spinors, J. Math. Phys. 21, 2567 (1980).Google Scholar
Ashtekar, A., New Perspectives in Canonical Gravity (Bibliopolis, Napoli, 1988).Google Scholar
Choquet-Bruhat, Y. and York, J.W., Jr., The Cauchy Problem, in General Relativity and Gravitation, vol. 1, ed. Held, A. (Plenum, New York, 1980).Google Scholar
Bergmann, P.G., Observables in General Relativity, Rev. Mod. Phys. 33, 510 (1961).Google Scholar
Bergmann, P.G., The General Theory of Relativity, in Handbuch der Physik, vol. IV, 4 ed. Flugge, S. (Springer, Berlin, 1962).Google Scholar
Bergmann, P.G. and Komar, A., Poisson Brackets between Locally Defined Observables in General Relativity, Phys. Rev. Lett. 4, 432 (1960)Google Scholar
Bergmann, P.G. and Komar, A., The Coordinate Group Symmetries of General Relativity, Int. J. Theor. Phys. 5, 15 (1972).Google Scholar
Wheeler, J.A., Geometrodynamics and the Issue of the Final State, in Relativity, Groups and Topology, eds. De Witt, B.S. and De Witt, C. (Gordon and Breach, London, 1964);Google Scholar
Wheeler, J.A., Superspace and the Nature of Quantum Geometrodynamics, in Battelle Rencontres 1967, eds. De Witt, C. and Wheeler, J.A. (Springer-Verlag, New York, 1968).Google Scholar
Fischer, A.E., The Theory of Superspace, in Relativity, eds. Carmeli, M., Fickler, L. and Witten, L. (Plenum, New York, 1970).Google Scholar
Fischer, A.E., The Unfolding of Singularities in Superspace, Gen. Rel. Grav. 15, 1191 (1983).Google Scholar
Fischer, A.E., Resolving the Singularities in the Space of Riemannian Geometries, J. Math. Phys. 27, 718 (1986).Google Scholar
Rainer, M., The Moduli Space of Local Homogeneous 3-Geometries, presentation at the Pacific Conference on Gravitation and Cosmology, Seoul 1996.Google Scholar
Timothy Swift, S., Natural Bundles: I. A Minimal Resolution of Superspace, J. Math. Phys. 33, 3723 (1992).Google Scholar
Timothy Swift, S., Natural Bundles: II. Spin and the diffeomorphism group, J. Math. Phys. 34, 3825 (1993).Google Scholar
Timothy Swift, S., Natural Bundles: III. Resolving the Singularities in the Space of Immersed Submanifolds, J. Math. Phys. 34, 3841 (1993).Google Scholar
Arms, J.M., Marsden, J.E. and Moncrief, V., Symmetry and Bifurcations of Momentum Mappings, Commun. Math. Phys. 78, 455 (1981).Google Scholar
Giulini, D., On the Configuration Space Topology in General Relativity, Helv. Phys. Acta 68, 86 (1995).Google Scholar
Lee, J. and Wald, R.M., Local Symmetries and Constraints, J. Math. Phys. 31, 725 (1990).Google Scholar
Beig, R., The Classical Theory of Canonical General Relativity, in Canonical Gravity: From Classical to Quantum, eds. Ehlers, J. and Friedrich, H. (Springer, Berlin, 1994).Google Scholar
Lichnerowicz, A., L’Integration des Equations de la Gravitation Relativiste et le Probleme des N Corps, J. Math. Pure Appl. 23, 37 (1944).Google Scholar
Choquet-Bruhat, Y., Sur l’Intgration des Equations d’Einstein, C. R. Acad. Sci. Paris 226, 1071 (1948).Google Scholar
Choquet-Bruhat, Y., The Cauchy Problem in Gravitation: An Introduction to Current Research, ed. Witten, L. (Wiley, New York, 1962).Google Scholar
York, J.W., Jr., Gravitational Degrees of Freedom and the Initial-Value Problem, Phys. Rev. Lett. 26, 1656 (1971).Google Scholar
York, J.W., Jr., Role of Conformal Three-Geometry in the Dynamics of Gravitation, Phys. Rev. Lett. 28, 1082 (1972).Google Scholar
York, J.W., Jr., Mapping onto Solutions of the Gravitational Initial Value Problem, J. Math. Phys. 13, 125 (1972)Google Scholar
York, J.W., Jr., Conformally Invariant Orthogonal Decomposition of Symmetric Tensors on Riemannian Manifolds and the Initial-Value Problem of General Relativity, J. Math. Phys. 14, 456 (1972)Google Scholar
York, J.W., Jr., Covariant Decompositions of Symmetric Tensors in the Theory of Gravitation, Ann. Ins. H. Poincare 21, 318 (1974).Google Scholar
O’Murchadha, N. and York, J.W., Jr., Existence and Uniqueness of Solutions of the Hamiltonian Constraint of General Relativity on Compact Manifolds, J. Math. Phys. 14, 1551 (1972)Google Scholar
O’Murchadha, N. and York, J.W., Jr., The Initial-Value Problem of General Relativity, Phys. Rev. D10, 428 (1974).Google Scholar
York, J.W. Jr., Kinematics and Dynamics of General Relativity, in Sources of Gravitational Radiation, ed. Smarr, L.L. (Cambridge University Press, Cambridge, 1979).Google Scholar
Qadir, A. and Wheeler, J.A., York’s Cosmic Time Versus Proper Time, in From SU(3) to Gravity, Y. Ne’eman’s Festschrift, eds. Gotsma, E. and Tauber, G. (Cambridge University Press, Cambridge, 1985).Google Scholar
McCarthy, P.J., Structure of the Bondi-Metzner-Sachs Group, J. Math. Phys. 13, 1837 (1972).Google Scholar
McCarthy, P.J., Representations of the Bondi-Metzner-Sachs Group I, Proc. Roy. Soc. London A330, 517 (1972).Google Scholar
McCarthy, P.J., Representations of the Bondi-Metzner-Sachs Group II, Proc. Roy. Soc. London A333, 317 (1973).Google Scholar
McCarthy, P.J., Asymptotically Flat Spacetimes and Elementary Particles, Phys. Rev. Lett. 29, 817 (1972).Google Scholar
McCarthy, P.J. and Crampin, M., Representations of the Bondi-Metzner-Sachs Group III: Poincare Spin Multiplicities and Irreducibility, Proc. Roy. Soc. London A335, 301 (1973).Google Scholar
Winicour, J., Angular Momentum in General Relativity, in General Relativity and Gravitation, vol. 2, ed. Held, A. (Plenum, New York, 1980).Google Scholar
Jaramillo, J.L. and Gourgoulhon, E., Mass and Angular Momentum in General Relativity, in Mass and Motion in General Relativity, eds. Blanchet, L., Spallicci, A., and Whiting, B., (Springer, Berlin, 2011).Google Scholar
Dirac, P.A.M., The Hamiltonian Form of Field Dynamics, Canad. J. Math. 3, 1 (1951).Google Scholar
Choquet-Bruhat, Y., Fischer, A., and Marsden, J.E., Maximal Hypersurfaces and Positivity of A New Proof of the Positive Energy Theorem Mass, in LXVII E.Fermi Summer School of Physics Isolated Gravitating Systems in General Relativity, ed. Ehlers, J. (North-Holland, Amsterdam, , 1979).Google Scholar
Frauendiener, J., Triads and the Witten Equation, Class. Quantum Grav. 8, 1881 (1991).Google Scholar
Sen, A., On the Existence of Neutrino Zero-Modes in Vacuum Spacetimes, J. Math. Phys. 22, 1781 (1981).Google Scholar
Sen, A., Gravity as a Spin System, Phys. Lett. 119B, 89 (1982).Google Scholar
Witten, E., A New Proof of the Positive Energy Theorem, Commun. Math. Phys. 80, 381 (1981).Google Scholar
Deser, S. and Isham, C.J., Canonical Vierbein Form of General Relativity, Phys. Rev. D14, 2505 (1976).Google Scholar
Isham, C.J., Canonical Quantum Gravity and the Problem of Time, in Integrable Systems, Quantum Groups and Quantum Field Theories, eds. Ibort, L.A. and Rodriguez, M.A. (Kluwer, London, 1993).Google Scholar
Isham, C.J., Conceptual and Geometrical Problems in Quantum Gravity, in Recent Aspects of Quantum Fields, eds. Mitter, H. and Gausterer, H. (Springer, Berlin, 1991).Google Scholar
Isham, C.J., Prima Facie Questions in Quantum Gravity and Canonical Quantum Gravity and the Question of Time, in Canonical Gravity: From Classical to Quantum, eds. Ehlers, J. and Friedrich, H. (Springer, Berlin, 1994).Google Scholar
Misner, C.W., Thorne, K.S., and Wheeler, J.A., Gravitation (Freeman, New York, 1973).Google Scholar
Weinberg, S., Gravitation and Cosmology (J. Wiley, New York, 1972).Google Scholar
Isenberg, J. and Nester, J., Canonical Gravity, in General Relativity and Gravitation, vol. 1, ed. Held, A. (Plenum, New York, 1980).Google Scholar
Rendall, A.D., Local and Global Existence Theorems for the Einstein Equations, Living Rev. Rel., 1, 4 (1998) and 3, 1 (2000) (arXiv gr-qc/0001008).Google Scholar
Friedrich, H. and Rendall, A.D., The Cauchy Problem for Einstein Equations, in Einstein’s Field Equations and their Physical Interpretation, ed. Schmidt, B.G. (Springer, Berlin, 2000).Google Scholar
Teitelboim, C., The Hamiltonian Structure of Space-Time, in General Relativity and Gravitation, vol 1, ed. Held, A., (Plenum, New York, 1980).Google Scholar
Kuchar, K., I: Geometry of Hyperspace, J. Math. Phys. 17, 777, (1976).Google Scholar
Kuchar, K., II: Kinematics of Tensor Fields in Hyperspace, J. Math. Phys. 17, 792 (1976).Google Scholar
Kuchar, K., III: Dynamics of Tensor Fields in Hyperspace, J. Math. Phys. 17, 801 (1976).Google Scholar
Kuchar, K., IV: Geometrodynamics with Tensor Sources, J. Math. Phys. 18, 1589 (1977).Google Scholar
Pons, J.M. and Shepley, L., Evolutionary Laws, Initial Conditions and Gauge Fixing in Constrained Systems, Class. Quantum Grav. 12, 1771 (1995) (arXiv gr-qc/9508052).Google Scholar
Pons, J.M., Salisbury, D.C., and Shepley, L.C., Gauge Transformations in the Lagrangian and Hamiltonian Formalisms of Generally Covariant Theories, Phys. Rev. D55, 658 (1997) (arXiv gr-qc/9612037).Google Scholar
Sugano, R., Kagraoka, Y., and Kimura, T., Gauge Transformations and Gauge-Fixing: Condition in Constraint System, Int. J. Mod. Phys. A7, 61 (1992).Google Scholar
Dittrich, B., Partial and Complete Observables for Hamiltonian Constrained Systems, Gen. Rel. Grav. 39, 1891 (2007) (arXiv gr-qc/0411013).Google Scholar
Dittrich, B., Partial and Complete Observables for Canonical General Relativity, Gen. Rel. Grav. 23, 6155 (2006) (arXiv gr-qc/0507106).Google Scholar
Dittrich, B., Hohn, P.A., Koslowski, T.A., and Nelson, M.I., Chaos, Dirac Observables and Constraint Quantization, preprint (2015) (arXiv 1508.01947).Google Scholar
Thiemann, T. Reduced Phase Space Quantization and Dirac Observables, Class.Quantum Grav. 23, 1163 (2006) (arXiv 0411031).Google Scholar
Pons, J.M., Salisbury, D.C., and Sundermeyer, K.A., Revisiting Observables in Generally Co-variant Theories in the Light of Gauge Fixing Methods, Phys. Rev. D80, 084015 (2009) (arXiv 0905.4564).Google Scholar
Pons, J.M., Salisbury, D.C., and Sundermeyer, K.A., Observables in Classical Canonical Gravity: Folklore Demystified (2010) (arXiv 1001.272).Google Scholar
Rovelli, C., Relational Quantum Mechanics, Int. J. Theor. Phys. 35, 1637 (1996) (arXiv quant-ph/9609002).Google Scholar
Rovelli, C. and Smerlak, M., Relational EPR, Found. Phys. 37, 427 (2007) (arXiv quant-ph/0604064).Google Scholar
Schwinger, J., Quantized Gravitational Field, Phys. Rev. 130, 1253 (1963).Google Scholar
Synge, J.L., Relativity: The General Theory (North-Holland, Amsterdam, 1964).Google Scholar
Stephani, H., General Relativity, 2nd edition (Cambridge University Press, Cambridge, 1996).Google Scholar
Schutz, B.F., A First Course in General Relativity (Cambridge University Press, Cambridge, 1985).Google Scholar
Thorne, K., Gravitational Radiation, in Three Hundred Years of Gravitation, ed. Hawking, S. and Israel, W. (Cambridge University Press, Cambridge, 1987).Google Scholar
Thorne, K., The Theory of Gravitational Radiation: An Introductory Review, in Gravitational Radiation, ed. Deruelle, N. and Piran, T. (North-Holland, Amsterdam, 1983).Google Scholar
Thorne, K., Multipole Expansions of Gravitational Radiation, Rev. Mod. Phys. 52, 299 (1980).Google Scholar
Pati, M.E. and Will, C.M., Post-Newtonian Gravitational Radiation and Equations of Motion via Direct Integration of the Relaxed Einstein Equations: Foundations, Phys. Rev. D62, 124015 (2000)Google Scholar
Pati, M.E. and Will, C.M., II: Two-Body Equations of Motion to Second Post-Newtonian Order and Radiation Reaction to 3.5 Post-Newtonian Order, Phys. Rev. D65, 104008 (2002).Google Scholar
Will, C., III: Radiation Reaction for Binary Systems with Spinning Bodies, Phys. Rev. D71, 084027 (2005).Google Scholar
Wang, H. and Will, C., IV: Radiation Reaction for Binary Systems with Spin-Spin Coupling, Phys. Rev. D75, 064017 (2007).Google Scholar
Mitchell, T. and Will, C., V: Evidence for the Strong Equivalence Principle in Second Post-Newtonian Order, Phys. Rev. D75, 124025 (2007).Google Scholar
Will, C.M., On the Unreasonable Effectiveness of the Post-Newtonian Approximation in Gravitational Physics, Proc. Nat. Acad. Sci. USA 108, 5938 (2011) (arXiv 1102.5192).Google Scholar
Damour, T. and Nagar, A., The Effective One Body Description of the Two-Body Problem (2009).Google Scholar
Damour, T., Introductory Lectures on the Effective One Body Formalism (2008) (arXiv 0802.4047).Google Scholar
Schaefer, G., Post-Newtonian Methods: Analytic Results on the Binary Problem, in Mass and Motion in General Relativity, Proceedings of the 2008 CNRS School in Orleans/France, eds. Blanchet, L., Spallicci, A., and Whiting, B. (Springer, Berlin, 2011) (arXiv 0910.2857).Google Scholar
Schaefer, G., The Gravitational Quadrupole Radiation-Reaction Force and the Canonical Formalism of ADM, Ann. Phys. (N.Y.) 161, 81 (1985).Google Scholar
Schaefer, G., The ADM Hamiltonian and the Postlinear Approximation, Gen. Rel. Grav. 18, 255 (1985).Google Scholar
Ledvinka, T., Schaefer, G., and Bicak, J., Relativistic Closed-Form Hamiltonian for Many-Body Gravitating Systems in the Post-Minkowskian Approximation, Phys. Rev. Lett. 100, 251101 (2008) (arXiv 0807.0214).Google Scholar
Ehlers, J. and Rundolph, E., Dynamics of Extended Bodies in General Relativity: Center-of-Mass Description and Quasi-Rigidity, Gen. Rel. Grav. 8, 197 (1977).Google Scholar
Beiglboeck, W., The Center of Mass in Einstein’s Theory of Gravitation, Commun. Math. Phys. 5, 106 (1967).Google Scholar
Schattner, R., The Center of Mass in General Relativity, Gen. Rel. Grav. 10, 377 (1978).Google Scholar
Schattner, R., The Uniqueness of the Center of Mass in General Relativity, Gen. Rel. Grav. 10, 395 (1979).Google Scholar
Ehlers, J. and Geroch, R., Equation of Motion of Small Bodies in Relativity, Ann. Phys. 309, 232 (2004).Google Scholar
Kopeikin, S. and Vlasov, I., Parametrized Post-Newtonian Theory of Reference Frames, Multipolar Expansions and Equations of Motion in the N-body Problem, Phys. Rep. 400, 209 (2004) (arXiv gr-qc/0403068).Google Scholar
Steinhoff, J. and Puetzfeld, D., Multipolar Equations of Motion for Extended Test Bodies in General Relativity (2009) (arXiv 0909.3756).Google Scholar
Flanagan, E.E. and Hughes, S.A., The Basics of Gravitational Wave Theory, New J. Phys. 7, 204 (2005) (arXiv gr-qc/0501041).Google Scholar
Mino, Y., Sasaki, M., and Tanaka, T., Gravitational Radiation Reaction to a Particle Motion, Phys. Rev. D55, 3457 (1997) (arXiv gr-qc/9606018).Google Scholar
Quinn, T.C. and Wald, R.M., Phys. Rev. D56, 3381 (1997) (arXiv gr-qc/9610053).Google Scholar
Detweiler, S. and Whiting, B.F., Self-Force via a Green’s Function Decomposition, Phys. Rev. D67, 024025 (2003) (arXiv gr-qc/0202086).Google Scholar
Wald, R.M., Introduction to Gravitational Self-Force, in Mass and its Motion, Proceedings of the 2008 CNRS School in Orleans/France, eds. Blanchet, L., Spallicci, A., and Whiting, B. (Springer, Berlin, 2011) (arXiv 0907.0412).Google Scholar
Gralla, S.E. and Wald, R.M., Derivation of Gravitational Self-Force, in Mass and its Motion, Proceedings of the 2008 CNRS School in Orleans/France, eds. Blanchet, L., Spallicci, A., and Whiting, B. (Springer, Berlin, 2011) (arXiv 0907.0414).Google Scholar
Pound, A., A New Derivation of the Gravitational Self-Force (2009) (arXiv 0907.5197).Google Scholar
Ciufolini, I. and Pavlis, E.C., A Confirmation of the General Relativistic Prediction of the Lense-Thirring Effect, Nature 431, 958 (2004).Google Scholar
Everitt, C.W.F. and Parkinson, B.W., Gravity Probe B Science Results: NASA Final Report (2008). Available online: http://einstein:stanford:edu/content/finalreport/GPBFinalNASAReport-020509-web.pdf.Google Scholar
Kopeikin, S.M. and Fomalont, E.B., Gravitomagnetism, Causality and Aberration of gravity in the Gravitational Light-Ray Detection Experiments, Gen. Rel. Grav. 39, 1583 (2007) (arXiv gr-qc/0510077).Google Scholar
Kopeikin, S.M. and Fomalont, E.B., Aberration and the Fundamental Speed of Gravity in the Jovian Detection Experiment, Found. Phys. 36, 1244 (2006) (arXiv astro-ph/0311063).Google Scholar
Kopeikin, S.M. and Makarov, V.V., Gravitational Bending of Light by Planetary Multipoles and its Measurement with Microarcsecond Astronomical Interferometers, Phys. Rev. D75, 062002 (2007) (arXiv astro-ph/0611358).Google Scholar
Carlip, S., Model-Dependence of Shapiro Time Delay and the “Speed of Gravity/Speed of Light” Controversy, Class. Quantum Grav. 21, 3803 (2004) (arXiv gr-qc/0403060).Google Scholar
Will, C., Propagation Speed of Gravity and the Relativistic Time Delay, Astrophys. J. 590, 683 (2003) (arXiv astro-ph/0301145).Google Scholar
Lindegren, L. and Dravins, D., The Fundamental Definition of ‘Radial Velocity’, Astron. Astrophys. 401, 1185 (2003) (arXiv astro-ph/0302522).Google Scholar
Teyssandier, P., Le Poncin-Lafitte, C., and Linet, B., A Universal Tool for Determining the Time Delay and the Frequency Shift of Light: Synge’s World Function, Astrophys. Space Sci. Libr. 349, 153 (2007) (arXiv 0711.0034).Google Scholar
Teyssandier, P. and Le Poncin-Lafitte, C., General Post-Minkowskian Expansion of Time Transfer Functions, Class. Quantum Grav. 25, 145020 (2008) (arXiv 0803.0277).Google Scholar
Bruegmann, M.H., Light Deflection in the Postlinear Gravitational Field of Bounded Pointlike Masses, Phys. Rev. D72, 024012 (2005) (arXiv grqc/0501095).Google Scholar
Harrison, E., The Redshift–Distance and Velocity–Distance Laws, Astrophys. J. 403, 28 (1993).Google Scholar
Bartelmann, M., The Dark Universe, Rev. Mod. Phys. 82, 331 (2010) (arXiv 0906.5036).Google Scholar
Bean, R., TASI Lectures on Cosmic Acceleration (2009) (arXiv 1003.4468).Google Scholar
Favata, M., Post-Newtonian Corrections to the Gravitational-Wave Memory for Quasi-Circular, Inspiralling Compact Binaries (2009) (arXiv 0812.0069).Google Scholar
Jaramillo, J.L., Kroon, J.A.V., and Gourgoulhon, E., From Geometry to Numerics: Interdisciplinary Aspects in Mathematical and Numerical Relativity, Class. Quantum Grav. 25, 093001 (2008).Google Scholar
Hinder, I., The Current Status of Binary Black Hole Simulations in Numerical Relativity, (2010) (arXiv 1001.5161).Google Scholar
Blanchet, L., Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries, Living Rev. Rel. 9, 4 (2006)Google Scholar
Blanchet, L., Post-Newtonian Theory and the Two-Body Problem (2009) (arXiv 0907.3596).Google Scholar
Damour, T., Gravitational Radiation and the Motion of Compact Bodies, in Gravitational Radiation, eds. Deruelle, N. and Piran, T. (North-Holland, Amsterdam, 1983).Google Scholar
Damour, T., The Problem of Motion in Newtonian and Einsteinian Gravity, in Three Hundred Years of Gravitation, eds. S. Hawking and W. Israel (Cambridge University Press, Cambridge, 1987).Google Scholar
Poisson, E., The Motion of Point Particles in Curved Space-Time, Living Rev. Rel. 7, 6 (2004) (arXiv gr-qc/0306052).Google Scholar
Poisson, E., Constructing the Self-Force, in Mass and its Motion, Proceedings of the 2008 CNRS School in Orleans/France, eds. Blanchet, L., Spallicci, A., and Whiting, B. (Springer, Berlin, 2011).Google Scholar
Infeld, L. and Plebanski, J., Motion ande Relativity, (Pergamon, Oxford, 1960).Google Scholar
Geroch, R. and Traschen, J., Strings and Other Distributional Sources in General Relativity, Phys. Rev. D36, 1017 (1987).Google Scholar
Steinbauer, R. and Vickers, J.A., The Use of Generalized Functions and Distributions in General Relativity, Class. Quantum Grav. 23, R91 (2006) (arXiv gr-qc/0603078).Google Scholar
Barducci, A., Casalbuoni, R., and Lusanna, L., Energy–Momentum Tensor of Extended Relativistic Systems, Nuovo Cim. 54A, 340 (1979).Google Scholar
Moni Bidin, C., Carraro, G., Me’ndez, G.A. and van Altena, W.F., No Evidence for a Dark Matter Disk within 4 kpc from the Galactic Plane (2010) (arXiv 1011.1289).Google Scholar
Damour T., T. and Deruelle, N., General Relativistic Celestial Mechanics of Binary Systems: I. The Post-Newtonian Motion, Ann. Inst.H. Poincaré 43, 107 (1985).Google Scholar
Damour T., T. and Deruelle, N., General Relativistic Celestial Mechanics of Binary Systems. II. The Post-Newtonian Timing Formula, Ann. Inst.H. Poincaré 44, 263 (1986).Google Scholar
Longair, M.S., Galaxy Formation (Springer, Berlin, 2008).Google Scholar
Ross, M., Dark Matter: The Evidence from Astronomy, Astrophysics and Cosmology (2010) (arXiv 1001.0316).Google Scholar
Garret, K. and Duda, G., Dark Matter: A Primer, Adv. Astron. 2011, 968283 (2011) (arXiv 1006.2483).Google Scholar
Schneider, P., Ehlers, J., and Falco, E.E., Gravitational Lenses (Springer, Berlin, 1992).Google Scholar
Bartelmann, M. and Schneider, P., Weak Gravitational Lensing, Phys.Rev. D340, 291 (2001) (arXiv astro-ph/9912508).Google Scholar
Battaner, E. and Florido, E., The Rotation Curve of Spiral Galaxies and its Cosmological Implications, Fund. Cosmic Phys. 21, 1 (2000) (arXiv astroph/0010475).Google Scholar
Banhatti, D.G., Disk Galaxy Rotation Curves and Dark Matter Distribution, Curr. Sci. 94, 986 (2008) (arXiv astro-ph/0703430).Google Scholar
de Blok, W.J.G. and Bosma, A., High Resolution Rotation Curves of Low Surface Brightness Galaxies, Astron. Astrophys. 385, 816 (2002) (arXiv astroph/0201276).Google Scholar
Milgrom, M., New Physics at Low Accelerations (MOND): An Alternative to Dark Matter, (2009) (arXiv 0912.2678).Google Scholar
Capozziello, S., Cardone, V.F., and Troisi, A., Low Surface Brightness Galaxies Rotation Curves in the Low Energy Limit of Rn Gravity: No Need for Dark Matter?, Mon. Not. R. Astron. Soc. 375, 1423 (2007) (arXiv astro-ph/0603522).Google Scholar
Feng, J.L., Dark Matter Candidates from Particle Physics and Methods of Detection, (2010) (arXiv 1003.0904).Google Scholar
Cooperstock, F.I. and Tieu, S., General Relativistic Velocity: The Alternative to Dark Matter, Mod. Phys. Lett. A23, 1745 (2008) (arXiv 0712.0019).Google Scholar
Kovalevski, J., Mueller, I.I., and Kolaczek, B., Reference Frames in Astronomy and Geophysics (Kluwer, Dordrecht, 1989).Google Scholar
Sovers, O.J. and Fanselow, J.L., Astrometry and Geodesy with Radio Interferometry: Experiments, Models, Results, Rev. Mod. Phs. 70, 1393 (1998).Google Scholar
Ma, C., Arias, E.F., Eubanks, T.M., et al., The International Celestial Reference Frame as Realized by Very Long Baseline Interferometry, Astron. J. 116, 516 (1998).Google Scholar
Johnstone, K.J. and de Vegt, Chr., Reference Frames in Astronomy, Ann. Rev. Astron. Astrophys. 37, 97 (1999).Google Scholar
Fey, A., Gordon, G., and Jacobs, C. (eds.), The Second Realization of the International Celestial Reference Frame by Very Long Baseline Interferometry, IERS Technical Note 35 (2009).Google Scholar
UCLA, The ABC’s of Distances (2007). Available online: http://www.astro.ucla.edu/wright/distance:htm.Google Scholar
Carroll, B.W. and Ostlie, D.A., An Introduction to Modern Astrophysics, 2nd edition (Pearson, Upper Saddle River, NJ, 2007).Google Scholar
Anderson, J.L. and Bergmann, P.G., Constraints in Covariant Field Theories, Phys. Rev. 83, 1018 (1951).Google Scholar
Bergmann, P.G. and Goldberg, J., Dirac Bracket Transformations in Phase Space, Phys. Rev. 98, 531 (1955).Google Scholar
Gotay, M.J., Nester, J.M., and Hinds, G., Presymplectic Manifolds and the Dirac-Bergmann Theory of Constraints, J. Math. Phys. 19, 2388 (1978).Google Scholar
Gotay, M.J. and Nester, J.M., Presymplectic Lagrangian Systems. I: The Constraint Algorithm and the Equivalence Theorem, Ann. Inst. Henri Poincaré A30, 129 (1979).Google Scholar
Gotay, M.J. and Nester, J.M., Presymplectic Lagrangian Systems. II: The Second-Order Equation Problem, Ann. Inst. Henri Poincaré A32, 1 (1980).Google Scholar
Battle, C., Gomis, J., Pons, J.M., and Roma’n-Roy, N., Equivalence between the Lagrangian and Hamiltonian Formalism for Constrained Systems, J. Math. Phys. 27, 2953 (1986).Google Scholar
Echeverri’a-Enri’quez, A., Muñoz-Lecanda, M.C., and Roma’n-Roy, N., Reduction of Presymplectic Manifolds with Symmetry, Rev. Math. Phys. 11, 1209 (1999)Google Scholar
Echeverri’a-Enri’quez, A., Muñoz-Lecanda, M.C., and Roma’n-Roy, N., A Geometrical Analysis of the Field Equations in Field Theory, Int. J. Math. Meth. Sc. 29, 687 (2002) (arXiv math-ph/0105018).Google Scholar
Echeverri’a-Enri’quez, A., Muñoz-Lecanda, M.C., and Roma’n-Roy, N., Geometry of Multisymplectic Hamiltonian First-Order Field Theories, J. Math. Phys. 41, 7402 (2000) (arXiv math-ph/0004005).Google Scholar
de Le’on, M., Mari’n-Solano, J., Marrero, J.C., Muñoz-Lecanda, M.C., and Roma’n-Roy, N., Singular Lagrangian Systems on Jet Bundles, Fortsch. Phys. 50, 105 (2002).Google Scholar
Cendra, H., Etchechoury, M., and Ferraro, S.J., An Extension of the Dirac and Gotay–Nester Theories of Constraints for Dirac Dynamical Systems, J. Geom. Mech. 6, 167 (2014) (arXiv 1106.3354).Google Scholar
Schmidt, R., Infinite Dimensional Hamiltonian Systems (Bibliopolis, Napoli, 1987).Google Scholar
Gantmacher, F., Lectures in Analytical Mechanics (Mir, Moscow, 1970).Google Scholar
Arnold, V.I., Mathematical Methods of Classical Mechanics (Springer, New York, 1978).Google Scholar
Liebermann, P. and Marle, C.M., Symplectic Geometry and Analytical Mechanics (Reidel, Dordrecht, 1987).Google Scholar
Nakahara, M., Geometry, Topology and Physics (Institute of Physics Publishing, Bristol, 1990)Google Scholar
Lusanna, L., An Enlarged Phase Space for Finite-Dimensional Constrained Systems, Unifying Their Lagrangian, Phase- and Velocity-Space Descriptions, Phys. Report 185, 1 (1990).Google Scholar
Barbashov, B.M. and Nesterenko, V.V., Continuous Symmetries in Field Theory, Fortschr. Phys. 31, 535 (1983).Google Scholar
Sarlet, W. and Cantrijn, F., Symmetries and Conservation Laws for Generalized Hamiltonian Systems, SIAM Rev. 23, 467 (1981).Google Scholar
Logan, J.D., Invariant Variational Principles (Academic Press, New York, 1977).Google Scholar
Konopleva, N.P. and Popov, V.N., Gauge Fields (Harwood, New York, 1981).Google Scholar
Cariñena, J.F., Lazaro-Cami, J.A. and Martinez, E., On Second Noether’s Theorem and Gauge Symmetries in Mechanics, Int. J. Geom. Meth. Mod. Phys. 3, 471 (2006) (arXiv math/0511180).Google Scholar
Candotti, E., Palmieri, C., and Vitale, B., On the Inversion of Noether’s Theorem in the Lagrangian Formalism, Nuovo Cimento 70, 233 (1970).Google Scholar
Candotti, E., Palmieri, C., and Vitale, B., Universal Noether’s Nature of Infinitesimal Transformations in Lorentz Covariant Field Theories, Nuovo Cimento A7, 271 (1972).Google Scholar
Anderson, R.L. and Ibragimov, N.H., Lie-Bäcklund Transformations in Applications (SIAM, Philadelphia, PA, 1979).Google Scholar
Marsden, J.E. and Weinstein, A., Reduction of Symplectic Manifolds with Symmetry, Rep. Math. Phys. 5, 121 (1974).Google Scholar
Sjamaar, R. and Lerman, E., Stratified Symplectic Spaces and Reduction, Ann. Math. 134, 375 (1991).Google Scholar
Lusanna, L., The Second Noether Theorem as the Basis of the Theory of Singular Lagrangians and Hamiltonian Constraints, Riv. Nuovo Cimento 14, 1 (1991).Google Scholar
Lusanna, L., The Shanmugadhasan Canonical Transformation, Function Groups and the Second Noether Theorem, Int. J. Mod. Phys. A8, 4193 (1993).Google Scholar
Lusanna, L., The Relevance of Canonical Transformations in Gauge Theories and General Relativity, Lecture Notes of Seminario Interdisciplinare di Matematica (Basilicata Univ.) 5, 125 (2006).Google Scholar
Lusanna, L., Classical Observables of Gauge Theories from the Multitemporal Approach, Contemp. Math. 132, 531 (1992).Google Scholar
Loran, F., Non-Abelianizable First Class Constraints, Commun. Math. Phys. 254, 167 (2005) (arXiv hep-th/0303014).Google Scholar
Cabo, A. and Martinez, D.L., On Dirac’s Conjecture for Hamiltonian Systems with First- and Second-Class Constraints, Phys. Rev. 42, 2726 (1990).Google Scholar
Chaichian, M., Louis Martinez, D., and Lusanna, L., Dirac’s Constrained Systems: The Classification of Second-Class Constraints, Ann. Phys. (N.Y.) 232, 40 (1994).Google Scholar
Beig, R., Asymptotic Structure of Isolated Systems, in Highlights in Gravitation and Cosmology, eds. Iyer, B.R., Kembhavi, A., Narlikar, J.V., and Vishveshwara, C.V. (Cambridge University Press, Cambridge, 1988).Google Scholar
Penrose, R., Asymptotic Properties of Fields and Space-Times, Phys. Rev. Lett. 10, 66 (1963).Google Scholar
Penrose, R., Zero Rest-Mass Fields Including Gravitation: Asymptotic Behavior, Proc. Roy. Soc. London A284, 159 (1965).Google Scholar
Geroch, R. and Horowitz, G.T., Asymptotically Simple does not Imply Asymptotically Minkowskian, Phys. Rev. Lett. 40, 203 (1978).Google Scholar
Geroch, R. and Xanthopoulous, B.C., Asymptotic Simplicity is Stable, J. Math. Phys. 19, 714 (1978).Google Scholar
Geroch, R., Structure of the Gravitational Field at Spatial Infinity, J. Math. Phys. 13, 956 (1972).Google Scholar
Sommers, P., The Geometry of the Gravitational Field at Spacelike Infinity, J. Math. Phys. 19, 549 (1978).Google Scholar
Cruściel, P., On the Structure of Spatial Infinity: The Geroch structure. J. Math. Phys. 30, 2090 (1990).Google Scholar
Cruściel, P., Geodesically Regular Ashtekar-Hansen Structures, J. Math. Phys. 30, 2094 (1990).Google Scholar
Bergmann, P.G., “Gauge-Invariant” Variables in General Relativity, Phys. Rev. 124, 274 (1961).Google Scholar
Friedrich, H., Gravitational Fields Near Space-like and Null Infinity, J. Geom. Phys. 24, 83 (1998).Google Scholar
Friedrich, H., On the Conformal Structure of Gravitational Fields in the Large, in Highlights in Gravitation and Cosmology, eds. Iyer, B.R., Kembhavi, A., Narlikar, J.V., and Vishveshwara, C.V. (Cambridge University Press, Cambridge, 1988).Google Scholar
Friedrich, H., Asymptotic Structure of Space-Time, in Recent Advances in General Relativity, eds. Janis, A.I. and Porter, J.R. (Birkhauser, Basel, 1992).Google Scholar
Frauendiener, J., Conformal Infinity, Liv. Rev. Rel. 3, 4 (2000).Google Scholar
Bicák, J., Radiative Spacetimes: Exact Approaches, in Relativistic Gravitation and Gravitational Radiation, eds. Marck, J.A. and Lasota, J.P. (Cambridge University Press, Cambridge, 1997).Google Scholar
Winicour, J., Radiative Space-Times: Physical Properties and Parameters, in Highlights in Gravitation and Cosmology, eds. Iyer, B.R., Kembhavi, A., Narlikar, J.V., and Vishveshwara, C.V. (Cambridge University Press, Cambridge, 1988).Google Scholar
Beig, R. and Schmidt, B.G., Einstein’s Equations Near Spatial Infinity, Commun. Math. Phys. 87, 65 (1982).Google Scholar
Beig, R., Integration of Einstein’s Equations Near Spatial Infinity, Proc. Roy. Soc. London A391, 295 (1984).Google Scholar
Bondi, H., Gravitational Waves in General Relativity, Nature 186, 535 (1960).Google Scholar
Bondi, H., van der Burg, M.G., and Metzner, A.W.K., Gravitational Waves in General Relativity VII: Waves from Isolated Axisymmetric Systems, Proc. Roy. Soc. London A269, 21 (1962).Google Scholar
Sachs, R.K., Gravitational Waves in General Relativity VI: The Outgoing Radiation Condition, Proc. Roy. Soc. London A264, 309 (1962).Google Scholar
Sachs, R.K., Gravitational Waves in General Relativity VIII: Waves in Asymptotically Flat Spacetimes, A270, 103 (1962).Google Scholar
Sachs, R.K., Asymptotic Symmetries in Gravitational Theory, Phys. Rev. 128, 2851 (1962).Google Scholar
McCarthy, P.J., Structure of the Bondi-Metzner-Sachs Group, J. Math. Phys. 13, 1837 (1972); Representations of the Bondi-Metzner-Sachs Group. I. Determination of the Representations and II. Properties and Classification of Representations, Proc. Roy. Soc. London A330, 517 (1972) and A333, 317 (1973); Asymptotically Flat Space-times and Elementary Particles, Phys. Rev. Lett. 29, 817 (1972).Google Scholar
McCarthy, P.J. and Crampin, M., Representations of the Bondi-MetznerSach Group, III, Proc. Roy. Soc. London A335, 301 (1973).Google Scholar
Isenberg, J. and Marsden, J.E., The York Map is a Canonical Transformation, J. Geom. Phys. 1, 85 (1984).Google Scholar
O’Murchadha, N., Total Energy Momentum in General Relativity, J. Math. Phys. 27, 2111 (1986).Google Scholar
Christodoulou, D. and O’Murchadha, N., The Boost Problem in General Relativity, Commun. Math. Phys. 80, 271 (1981).Google Scholar
Giulini, D., Kiefer, C., and Zeh, H.D., Symmetries, Superselection Rules and Decoherence, Phys. Lett. A199, 291 (1995) (arXiv gr-qc/9410029).Google Scholar
Hartle, J., Laflamme, R., and Marolf, D., Conservation Laws in the Quantum Mechanics of Closed Systems, Phys. Rev. D51, 7007 (1995).Google Scholar
Moncrief, V., Gribov Degeneracies: Coulomb Gauge Conditions and Initial Value Constraints, J. Math. Phys. 20, 579 (1979).Google Scholar
Cantor, M., Elliptic Operators and the Decomposition of Tensor Fields, Bull. Am. Math. Soc. 5, 235 (1981).Google Scholar
Hawking, S.W. and Horowitz, G.T., The Gravitational Hamiltonian, Action, Entropy and Surface Terma, Class. Quantum Grav. 13, 1487 (1996).Google Scholar
Marolf, D., Mass Superselection, Canonical Gauge Transformations and Asymptotically Flat Variational Principles, Class. Quantum Grav. 13, 1871 (1996).Google Scholar
Barbour, J., General Relativity as a Perfectly Machian Theory, in Mach’s Principle: From Newton’s Bucket to Quantum Gravity, eds. Barbour, J.B. and Pfister, H., (BirkHäuser, Boston, MA, 1995).Google Scholar
De Witt, B.S., Quantum Theory of Gravity, Phys. Rev. 160, 1113 (1967).Google Scholar
De Witt, B.S., Quantum theory of Gravity: II. The Manifestly Covariant Theory, Phys. Rev. 162, 1195 (1967).Google Scholar
De Witt, B.S., The Dynamical Theory of Groups and Fields (Gordon and Breach, New York, 1967).Google Scholar
Schoen, R. and Yau, S.T., Positivity of the Total Mass of a General Space-Time, Phys. Rev. Lett. 43, 1457 (1979).Google Scholar
Schoen, R. and Yau, S.T., On the Proof of the Positive Mass Conjecture in General Relativity, Commun. Math. Phys. 65, 45 (1979).Google Scholar
Schoen, R. and Yau, S.T., Proof of the Positive Mass Theorem. II, Commun. Math. Phys. 79, 231 (1980).Google Scholar
Witten, E., A New Proof of the Positive Energy Theorem, Commun. Math. Phys. 80, 381 (1981).Google Scholar
Choquet-Bruhat, Y., Positive Energy Theorems, in Relativity, Groups and Topology II, eds. De Witt, B.S. and Stora, R. (North-Holland, Amsterdam, 1984).Google Scholar
Horowitz, G.T., The Positive Energy Theorem and its Extensions, in Asymptotic Behaviour of Mass and Spacetime Geometry, ed. Flaherty, F.J. (Springer, Berlin, 1984).Google Scholar
Landau, L. and Lifschitz, E., The Classical Theory of Fields (Addison-Wesley, Cambridge, MA, 1951).Google Scholar
Wang, Y.L., Wu, Z.X., Pan, H.Z., Lu, W.T., Jiang, H., and Chen, L., The Limit of Noether Conserved Charges is the Number of Primary First-Class Constraints in a Constrained System, Commun. Theor. Phys. 58, 539 (2012).Google Scholar
Wang, Y.L., Xu, C.T., Jiang, H., Lu, W.T., and Pan, H.Z., The Dirac Conjecture and the Non-Uniqueness of Lagrangian, preprint (2013) (arXiv 1306.3580).Google Scholar
Sugano, R., Kagraoka, Y., and Kimura, T., Gauge Transformations and Gauge-Fixing: Condition in Constraint System, Int. J. Mod. Phys. 7, 61 (1992).Google Scholar
Faddeev, L.D. and Shatashvili, S.L., Realization of the Schwinger Term in the Gauss Law and the Possibility of Correct Quantization of a Theory with Anomalies, Phys. Lett. B167, 225 (1986).Google Scholar
Batalin, I.A. and Fradkin, E.S., Operator Quantization of Dynamical Systems with Irreducible First- and Second-Class Constraints, Phys. Lett. B180, 157 (1986).Google Scholar
Batalin, I.A. and Fradkin, E.S., Operational Quantization of Dynamical Systems Subject to Second Class Constraints, Nucl. Phys. B279, 514 (1987).Google Scholar
Batalin, I.A. and Tyutin, I.V., Existence Theorem for the Effective Gauge Algebra in the Generalized Canonical Formalism with Abelian Conversion of Second-Class Constraints, Int. J. Mod. Phys. A6, 3255 (1991).Google Scholar
Shanmugadhasan, S., Canonical Formalism for Degenerate Lagrangians, J. Math. Phys. 14, 677 (1973).Google Scholar
Fulp, R.O. and Marlin, J.A., Function Groups Associated with Constraint Submanifolds, Rep. Math. Phys. 18, 295 (1980).Google Scholar
Castellani, L., Dominici, D., and Longhi, G., Canonical Transformations and Quantization of Singular Lagrangian Systems, Nuovo Cimento 48A, 91 (1978).Google Scholar
Dominici, D. and Gomis, J., Poincaré–Cartan Integral Invariant and Canonical Transformations for Singular Lagrangians, J. Math. Phys. 21, 2124 (1980).Google Scholar
Lusanna, L., An Extension of the Second Noether Theorem, Nuovo Cimento B52, 141 (1979).Google Scholar
Bergmann, P.G., Non-Linear Field Theories, Phys. Rev. 75, 680 (1949).Google Scholar
Komar, A., Field Theoretic Constraint Formalism, Found. Phys. 15, 473 (1985).Google Scholar
Moncrief, V., Gribov Degeneracies: Coulomb Gauge Conditions and Initial Value Constraints, J. Math. Phys. 20, 579 (1979).Google Scholar
Lusanna, L., On the BRS’s, J. Math. Phys. 31, 428 (1990).Google Scholar
Steinhardt, P.J., Problems of Quantization in the Infinite Momentum Frame, Ann. Phys. (N.Y.) 128, 425 (1980).Google Scholar
Benguria, R., Cordero, P., and Teitelboim, C., Aspects of the Hamiltonian Dynamics of Interacting Gravitational Gauge and Higgs Fields with Applications to Spherical Symmetry, Nucl. Phys. B122, 61 (1977).Google Scholar
Seiler, W.M. and Tucker, R.W., Involution and Constrained Dynamics I: The Dirac Approach, J. Phys. A28, 4431 (1995).Google Scholar
Utiyama, R., Invariant Theoretical Interpretation of Interaction, Phys. Rev. 101, 1597 (1956)Google Scholar
Utiyama, R., Theory of Invariant Variation and the Generalized Canonical Dynamics, Prog. Theor. Phys. Suppl. 9, 19 (1959).Google Scholar
Trautman, A., Conservation Laws in General Relativity, in Gravitation, ed. Witten, L. (Wiley, New York, 1962).Google Scholar
Trautman, A., Foundations and Current Problems of General Relativity, in Lectures on General Relativity, Brandeis Summer Institute in Theoretical Physics (Prentice Hall, Englewood Cliffs, 1964).Google Scholar
Karatas, D.L. and Kowalski, K.L., Noether’s Theorem for Local Gauge Transformations, Am. J. Phys. 58, 123 (1990).Google Scholar
Al-Kuwari, H.A. and Taha, M.O., Noether Theorem and Local Gauge Invariance, Am. J. Phys. 59, 363 (1991).Google Scholar
Brading, K. and Brown, H.R., Noether’s Theorems and Gauge Symmetries, preprint (2000), (arXiv hep-th/0009058).Google Scholar
Crosta, M., Gianmaria, M., Lattanzi, M.G., and Poggio, E., Shedding Light on the Milky Way Rotation Curve with Gaia DR2 (2018) (arXiv 1810.04445)Google Scholar
Ellis, G.F.R. and van Elst, H., Cosmological Models, Cargese Lectures 1998, NATO Adv. Stud. Inst. Ser. C. Math. Phys. Sci. 541, 1 (1999) (arXiv gr-qc/9812046).Google Scholar
Ellis, G.F.R., Inhomogeneity Effects in Cosmology (2011) (arXiv 1103.2335).Google Scholar
Clarkson, C., Ellis, G.F.R., Faltenbacher, A., Maartens, R., Umeh, O., and Uzan, J.P., (Mis-)Interpreting Supernovae Observations in a Lumpy Universe (2011) (arXiv 1109.2484).Google Scholar
Buchert, T. and Ellis, G.F.R., The Universe Seen at Different Scales, Phys. Lett. A 347, 38 (2005) (arXiv gr-qc/0506106).Google Scholar
Maartens, R., Is the Universe Homogeneous? (2011) (arXiv 1104.1300).Google Scholar
Tsagas, C.G., Challinor, A. and Maartens, R., Relativistic Cosmology and Large-Scale Structure, Phys. Rep. 465, 61 (2008) (arXiv 0705.4397).Google Scholar
Clarkson, C. and Maartens, R., Inhomogeneity and the Foundations of Concordance Cosmology, Class. Quantum Grav. 27, 124008 (2010) (arXiv 1005.2165).Google Scholar
Durrer, R., What Do We Really Know about Dark Energy? (2011) (arXiv 1103.5331).Google Scholar
Bonvin, C. and Durrer, R., What Galaxy Surveys Really Measure (2011) (arXiv 1105.5280).Google Scholar
Nakamura, K., Second-Order Gauge-Invariant Cosmological Perturbation Theory: Current Status, Ad. Astron. 2010, 576273 (2010) (arXiv 1001.2621).Google Scholar
Bonnor, W.B., Sulaiman, A.H., and Tanimura, N., Szekeres’s Space-Times have no Killing Vectors, Gen. Rel. Grav. 8, 549 (1977).Google Scholar
Berger, B.K., Eardley, D.M., and Olson, D.W., Notes on the Spacetimes of Szekeres, Phys. Rev. D16, 3086 (1977).Google Scholar
Nwankwo, A., Ishak, M., and Thomson, J., Luminosity Distance and Redshift in the Szekeres Inhomogeneous Cosmological Models (2010) (arXiv 1005.2989).Google Scholar
Plebański, J. and Krasiński, A., An Introduction to General Relativity and Cosmology (Cambridge University Press, Cambridge, 2006).Google Scholar
Celerier, M.N., Effects of Inhomogeneities on the Expansion of the Universe: A Challenge to Dark Energy? (2012) (arXiv 1203.2814).Google Scholar
Buchert, T., Dark Energy from Structure: A Status Report, Gen. Rel. Grav. 40, 467 (2008) (arXiv 0707.2153).Google Scholar
Wiegand, A. and Buchert, T., Multiscale Cosmology and Structure-Emerging Dark Energy: A Plausibility Analysis, Phys. Rev. D82, 023523 (2010) (arXiv 1002.3912).Google Scholar
Larena, J., Spatially Averaged Cosmology in an Arbitrary Coordinate System, Phys. Rev. D79, 084006 (2009) (arXiv 0902.3159).Google Scholar
van den Hoogen, R.J., Averaging Spacetime: Where Do We Go from Here? (2010) (arXiv 1003.4020).Google Scholar
Räsänen, S., Backreaction: Directions of Progress, Class. Quantum Grav. 28, 164008 (2011) (arXiv 1102.0408).Google Scholar
Buchert, T. and Räsänen, S., Backreaction in Late-Time Cosmology, Ann. Rev. Nucl. Particle Sci. 62, 57 (2012) (arXiv 1112.5335).Google Scholar
Wiltshire, D.L., What is Dust? Physical Foundations of the Averaging Problem in Cosmology (2011) (arXiv 1106.1693).Google Scholar
Fatibene, L., Ferraris, M., Francaviglia, M., and Lusanna, L., ADM Pseudotensors, Conserved Quantities and Covariant Conservation Laws in General Relativity, Ann. Phys. 327, 1593 (2012) (arXiv 1007.4071).Google Scholar
Henneaux, M., Nelson, J.E., and Schomblond, C., Derivation of Ashtekar Variables from Tetrad Gravity, Phys. Rev. D39, 434 (1989).Google Scholar
Lusanna, L., Canonical Gravity and Relativistic Metrology: From Clock Synchronization to Dark Matter as a Relativistic Inertial Effect (2012) (arXiv 1108.3224, version 1).Google Scholar
Torre, C.G. and Varadarajan, M., Functional Evolution of Free Quantum Fields, Class. Quantum Grav. 16, 2651 (1999)Google Scholar
Torre, C.G. and Varadarajan, M., Quantum Fields at Any Time, Phys. Rev. D58, 064007 (1998).Google Scholar
Pauri, M. and Prosperi, G.M., Canonical Realizations of Lie Symmetry Groups, J. Math. Phys. 7, 366 (1966).Google Scholar
Marmo, G., Saletan, E.J., Simoni, A., and Vitale, B., Dynamical Systems: A Differential Geometric Approach to Symmetry and Reduction (Wiley, Chicester, 1985).Google Scholar
Abraham, M. and Marsden, J.M., Foundations of Mechanics, 2nd edition (Benjamin, Reading, MA, 1979).Google Scholar
Souriau, J.M., Structure des syste’mes dynamiques (Dunod, Paris, 1970).Google Scholar
Niederer, U.H. and O’Raifeartaigh, L., Realizations of the Unitary Representations of the Inhomogeneous Space-Time Groups I: General Structure, Fortschr. Phys. 22, 111 (1974).Google Scholar
Niederer, U.H. and O’Raifeartaigh, L., Realizations of the Unitary Representations of the Inhomogeneous Space-Time Groups II: Covariant Realizations of the Poincaré Group, Fortschr. Phys. 22, 131 (1974).Google Scholar
Niederer, U.H., Massless Fields as Unitary Representations of the Poincaré Group, Fortschr. Phys. 27, 191 (1979).Google Scholar
Mackey, G., Induced Representations of Groups and Quantum Mechanics (Benjamin, New York, 1968).Google Scholar
Wigner, E., On Unitary Representations of the Inhomogeneous Lorentz Group, Ann. Math. 40, 149 (1939)Google Scholar
Wigner, E., Group Theory (Academic Press, New York, 1959).Google Scholar
Dominici, D., Gomis, J., and Longhi, G., A Lagrangian for Two Interacting Relativistic Particles: Canonical Formulation, Nuovo Cimento 48A, 257 (1978).Google Scholar
Weinberg, S., Feynman Rules for Any Spin, Phys. Rev. 133B, 1318 (1964).Google Scholar
D’Emma, G.C., On Quantization of the Electromagnetic Field, Helv. Phys. Acta 53, 535 (1980).Google Scholar
Han, D., Kim, Y.S., and Son, D., Photon Spin as a Rotation in Gauge Space, Phys. Rev. D25, 461 (1982).Google Scholar
Weinberg, S., Photons and Gravitons in S-Matrix Theory: Derivation of Charge Conservation and Equality of Gravitational and Inertial Mass, Phys. Rev. 135B, 1049 (1964).Google Scholar
Ohnuki, Y., Unitary Representations of the Poincare Group and Relativistic Wave Equations (World Scientific, Singapore, 1988).Google Scholar
Berezin, F.A. and Marinov, M.S., Particle Spin Dynamics as the Grassmann Variant of Classical Mechanics, Ann. Phys. (N.Y.) 104, 336 (1977).Google Scholar
Casalbuoni, R., On the Quantization of Systems with Anticommuting Variables, Nuovo Cimento 33A, 115 (1976).Google Scholar
Casalbuoni, R., The Classical Mechanics for Bose-Fermi Systems, Nuovo Cimento 33A, 389 (1976).Google Scholar
Barducci, A., Bordi, F., and Casalbuoni, R., Path Integral Quantization of Spinning Particles Interacting with Crossed External Electromagnetic Fields, Nuovo Cimento 64B, 287 (1986).Google Scholar
Barducci, A., Casalbuoni, R., and Lusanna, L., Anticommuting Variables, Internal Degrees of Freedom, and the Wilson Loop, Nucl. Phys. B180, 141 (1981).Google Scholar
Barducci, A., Buccella, F., Casalbuoni, R., Lusanna, L., and Sorace, E., Quantized Grassmann Variables and Unified Theories, Phys. Lett. 67B, 344 (1977)Google Scholar
Barducci, A., Buccella, F., Casalbuoni, R., Lusanna, L., and Sorace, E., Fermi Oscillators for Vectorlike Unified Theories with Unitary Groups, Lett. Nuovo Cimento 19, 335 (1977).Google Scholar
Barducci, A., Casalbuoni, R., and Lusanna, L., A Possible Interpretation of Theories Involving Grassmann Variables, Lett. Nuovo Cimento 19, 581 (1977).Google Scholar
Gomis, J. and Novell, M., Pseudoclassical Description for a Nonrelativistic Spinning Particle: II. Classical Content, Phys. Rev. D33, 2220 (1986).Google Scholar
Blanchet, L., Damour, T., and Schäfer, G., Post-Newtonian Hydrodynamics and Post-Newtonian Gravitational Wave Generation for Numerical Relativity, Mon. Not. R. Astr. Soc. 242, 289 (1990).Google Scholar
Asada, H., Shibata, M., and Futamase, T., Post-Newtonian Hydrodynamic Equations Using the (3+1) Formalism in General Relativity, Osaka University preprint (1996) (arXiv gr-qc/9606041).Google Scholar
Brown, J.D. and Kuchar, K., Dust as a Standard of Space and Time in Canonical Quantum Gravity, Phys. Rev. D51, 5600 (1995).Google Scholar
Maartens, R., Causal Thermodynamics in Relativity, Lectures at the H.Rund Workshop on Relativity and Thermodynamics (1996) (arXiv astreoph/9609119).Google Scholar
Smarr, L., Taubes, C., and Wilson, J.R., General Relativistic Hydrodynamics: The Comoving, Eulerian and Velocity Potential Formalisms, in Essays in General Relativity: A Festschrift for Abraham Taub, ed. Tipler, F.J. (Academic Press, New York, 1980).Google Scholar
Carter, B., Covariant Theory of Conductivity in Ideal Fluid or Solid Media, in Relativistic Fluid Dynamics, eds. Anile, A. and Choquet-Bruhat, Y. (Springer, Berlin, 1989).Google Scholar
Karsch, F. and Miller, D.E., Covariant Structure of Relativistic Gases in Equilibrium, Phys. Rev. D24, 2564 (1981).Google Scholar
Stewart, J.M., Non-Equilibrium Relativistic Kinetic Theory, (Springer, Berlin, 1971).Google Scholar
Hakim, R., Remarks on Relativistic Statistical Mechanics: I, J. Math. Phys. 8, 1315, (1967).Google Scholar
Hakim, R., Relativistic Kinetic Equations Including Radiation Effects: I. Vlasov Approximation, J. Math. Phys. 8, 1379 (1967).Google Scholar
Synge, J.L., The Relativistic Gas (North-Holland, Amsterdam, 1957).Google Scholar
van Weert, Ch. G., Some Problems in Relativistic Hydrodynamics, in Relativistic Fluid Dynamics, eds. Anile, A. and Choquet-Bruhat, Y. (Springer, Berlin, 1989).Google Scholar
Lindblom, L., The Relaxation Effect in Dissipative Relativistic Fluid Theories, Ann. Phys. (N.Y.) 247, 1 (1996).Google Scholar
Anile, A.M., Pavón, D., and Romano, V., The Case for Hyperbolic Theories of Dissipation in Relativistic Fluids (1998) (arXiv gr-qc/9810014).Google Scholar
Anile, A.M., Relativistic Fluids and Magnetofluids (Cambridge University Press, Cambridge, 1989).Google Scholar
Martí, J.M. and Müller, E., Numerical Hydrodynamics in Special Relativity (1990) (arXiv astro-ph/9906333).Google Scholar
J.Font, A., Stergioulas, N., and Kokkotas, K.D., Nonlinear Hydrodynamical Evolution of Rotating Relativistic Stars: Numerical Methods and Code Tests (1999) (arXiv gr-qc/9908010).Google Scholar
Baumgarte, T.W., Hughes, S.A., Rezzolla, L., Shapiro, S.L., and Shibata, M., Implementing Fully Relativistic Hydrodynamics in Three Dimensions (1999) (arXiv gr-qc/9907098).Google Scholar
Geroch, R. and Lindblom, L., Causal Theories of Dissipative Relativistic Fluids, Ann. Phys. (N.Y.) 207, 394 (1991).Google Scholar
Liu, I., Müller, I., and Ruggeri, T., Relativistic Thermodynamics of Gases, Ann. Phys. (N.Y.) 169, 191 (1986).Google Scholar
Geroch, R. and Lindblom, L., Dissipative Relativistic Fluid Theories of Divergence Type, Phys. Rev. D41, 1855 (1990).Google Scholar
Calzetta, E., Relativistic Fluctuating Hydrodynamics, Class. Quantum Grav. 15, 653 (1998) (arXiv gr-qc/9708048).Google Scholar
Müller, I., Zum Paradoxon der Wrmeleitungstheorie, Z. Phys. 198, 329 (1967).Google Scholar
Israel, W., Nonstationary Irreversible Thermodynamics: A Causal Relativistic Theory, Ann. Phys. (N.Y.) 100, 310 (1976).Google Scholar
Israel, W. and Stewart, J.M., Transient Relativistic Thermodynamics and Kinetic Theory, Ann. Phys. (N.Y.) 118, 341 (1979).Google Scholar
Jou, D., Leblon, G., and Casas Vasquez, J., Extended Thermodynamics, 2nd edition (Springer, Heidelberg, 1996).Google Scholar
Müller, I. and Ruggeri, T., Rational Extended Thermodynamics, 2nd edition (Springer, Berlin, 1998).Google Scholar
Peitz, J. and Appl, S., 3+1 Formulation of Non-Ideal Hydrodynamics, Class. Quantum Grav. 16, 979 (1999) (arXiv gr-qc/9710107).Google Scholar
Uzan, J.P., Dynamics of Relativistic Interacting Gases: From a Kinetic to a Fluid Description, Class. Quantum Grav. 15, 1063 (1998).Google Scholar
Uzan, J.P., Comment on Dynamics of Relativistic Interacting Gases, Class. Quantum Grav. 15, 3737 (1998).Google Scholar
Stewart, J.M., Comment: The Dynamics of Relativistic Interacting Gases, Class. Quantum Grav. 15, 3731 (1998).Google Scholar
Morrison, P.J., A Paradigm for Joined Hamiltonian and Dissipative Systems, Physica 18D, 410 (1986).Google Scholar
Nosé, S., A Unified Formulation of the Constant Temperature Molecular Dynamics Methods, J. Chem. Phys. 81, 511 (1984).Google Scholar

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