Geometric and Topological Methods for Quantum Field Theory Proceedings of the 2009 Villa de Leyva Summer School
Book contents
- Frontmatter
- Contents
- List of contributors
- Introduction
- 1 A brief introduction to Dirac manifolds
- 2 Differential geometry of holomorphic vector bundles on a curve
- 3 Paths towards an extension of Chern–Weil calculus to a class of infinite dimensional vector bundles
- 4 Introduction to Feynman integrals
- 5 Iterated integrals in quantum field theory
- 6 Geometric issues in quantum field theory and string theory
- 7 Geometric aspects of the Standard Model and the mysteries of matter
- 8 Absence of singular continuous spectrum for some geometric Laplacians
- 9 Models for formal groupoids
- 10 Elliptic PDEs and smoothness of weakly Einstein metrics of Hölder regularity
- 11 Regularized traces and the index formula for manifolds with boundary
- Index
- References
2 - Differential geometry of holomorphic vector bundles on a curve
Published online by Cambridge University Press: 05 May 2013
Book contents
- Frontmatter
- Contents
- List of contributors
- Introduction
- 1 A brief introduction to Dirac manifolds
- 2 Differential geometry of holomorphic vector bundles on a curve
- 3 Paths towards an extension of Chern–Weil calculus to a class of infinite dimensional vector bundles
- 4 Introduction to Feynman integrals
- 5 Iterated integrals in quantum field theory
- 6 Geometric issues in quantum field theory and string theory
- 7 Geometric aspects of the Standard Model and the mysteries of matter
- 8 Absence of singular continuous spectrum for some geometric Laplacians
- 9 Models for formal groupoids
- 10 Elliptic PDEs and smoothness of weakly Einstein metrics of Hölder regularity
- 11 Regularized traces and the index formula for manifolds with boundary
- Index
- References
Summary
A summary is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.
- Type
- Chapter
- Information
- Geometric and Topological Methods for Quantum Field TheoryProceedings of the 2009 Villa de Leyva Summer School, pp. 39 - 80Publisher: Cambridge University PressPrint publication year: 2013
References
[AB83] and . The Yang–Mills equations over Riemann surfaces. Phil. Trans. R. Soc. Lond.A 308 (1505): 523–615, 1983.Google Scholar
[Ati57] . Vector bundles over an elliptic curve. Proc. Lond. Math. Soc. 7 (3): 414–452, 1957.Google Scholar
[BT82] and . Differential forms in algebraic topology, Graduate Texts in Mathematics 82. New York: Springer-Verlag, 1982.
[DK90] and . The geometry of four-manifolds. Oxford Mathematical Monographs. Oxford: Clarendon Press; New York: Oxford University Press, 1990. Oxford Science Publications.
[Don83] . A new proof of a theorem of Narasimhan and Seshadri. J. Diff. Geom. 18 (2): 269–277, 1983.Google Scholar
[For91] . Lectures on Riemann surfaces, Graduate Texts in Mathematics 81. New York: Springer-Verlag, 1991. Translated from the 1977 German original by . Reprint of the 1981 English translation.
[Gro57] . Sur la classification des fibres holomorphes sur la sphère de Riemann. Am. J. Math. 79 : 121–138, 1957.Google Scholar
[Gun66] . Lectures on Riemann surfaces. Princeton, NJ: Princeton University Press, 1966.
[Hat02] . Algebraic topology. Cambridge: Cambridge University Press, 2002.
[Hus93] . Fibre bundles, 3rd edn. Berlin: Springer-Verlag, 1993.
[KN96] and . Foundations of differential geometry, Vol. I. Wiley Classics Library. New York: John Wiley & Sons Inc., 1996. Reprint of the 1963 original.
[Kob87] . Differential geometry of complex vector bundles. Princeton, NJ: Princeton University Press; Tokyo: Iwanami Shoten Publishers, 1987.
[LPV85] and . Variété de modules de fibres stables sur une surface de Riemann: résultats d'Atiyah et Bott. In Moduli of stable bundles over algebraic curves (Paris, 1983), Progress in Mathematics 5. Boston, MA: Birkhäuser Boston, 1985, pp. 5–28.
[MFK93] , , and . Geometric invariant theory, 3rd enl. ed.Berlin: Springer-Verlag, 1993.
[MS98] and . Introduction to symplectic topology, 2nd edn. Oxford Mathematical Monographs. Oxford: Clarendon Press; New York: Oxford University Press, 1998.
[Muk03] . An introduction to invariants and moduli, tran., . Cambridge: Cambridge University Press, 2003.
[Mum63] . Projective invariants of projective structures and applications. In Proceedings of the International Congress of Mathematicians (Stockholm, 1962), Djursholm: Institut Mittag-Leffler, 1963, pp. 526–530.
[New09] . Geometric invariant theory. In Moduli spaces and vector bundles, London Mathematical Society Lecture Note Series 359. Cambridge: Cambridge University Press, 2009, pp. 99–127.
[NS65] and . Stable and unitary vector bundles on a compact Riemann surface. Ann. Math. (2)82 : 540–567, 1965.Google Scholar
[Ses67] . Space of unitary vector bundles on a compact Riemann surface. Ann. Math. (2)85 : 303–336, 1967.Google Scholar
[Ses82] . Fibres vectoriels sur les courbes algébriques, volume 96 of Astérisque. Paris: Société Mathématique de France, 1982. Notes written by from a course at the École Normale Supérieure, June 1980.
[Ste51] . The topology of fibre bundles. Princeton, NJ: Princeton University Press, 1951.
[Tha97] . An introduction to the topology of the moduli space of stable bundles on a Riemann surface. et al. (eds), Geometry and physics: Proceedings of the conference at Aarhus University, Aarhus, Denmark, 1995. Lecture Notes in Pure and Applied Mathematics 184. New York: Marcel Dekker, 1997, pp. 71–99.
[Tho06] . Notes on GIT and symplectic reduction for bundles and varieties. In Surveys in differential geometry, Vol. 10, Somerville, MA: International Press, 2006, pp. 221–273.
[Wel08] Differential analysis on complex manifolds. With a new appendix by Oscar Garcia-Prada, 3rd edn. New York: Springer, 2008.
- 1
- Cited by