Book contents
- Frontmatter
- Contents
- The network
- Preface
- The constraint algebra of higher dimensional Chern-Simons theories
- Nonrelativistic Chern-Simons vortices from the constrained Hamiltonian formalism
- Classical solutions of gravitating Chern-Simons electrodynamics
- Exponentially localised instantons in a hierarchy of Higgs models
- Obstructions to ganging WZ terms: a symplectic curiosity
- Global aspects of symmetries in sigma models with torsion
- Canonical structure of the non-linear σ-model in a polynomial formulation
- A manifestly gauge-invariant approach to quantum theories of gauge fields
- On the Hamiltonian formulation of higher dimensional Chern-Simons gravity
- An Example of Loop Quantization
- Gauge fixing in constrained systems
- Light-cone formulation of gauge theories
- Hamiltonian constraints and Dirac observables
- Gauging kinematical and internal symmetry groups for extended systems
- On the harmonic interaction of three relativistic point particles
- Non existence of static multi-black-hole solutions in 2+1 dimensions
- Spherically symmetric gravity and the notion of time in general relativity
- Canonical decomposition of Belinskii-Zakharov one-soliton solutions
- Hamiltonian reduction and the R-matrix of the Calogero model
- Intrinsic approach to the Legendre transformation in super-mechanics
- Field-antifield description of anomalous theories
- Transfer matrix quantization of general relativity, and the problem of time
- The W3-particle
- Pure geometrical approach to singular Lagrangians with higher derivatives
- Dirac versus reduced phase space quantization
- Classical and quantum aspects of degenerate metric fields
- BRST-antibracket cohomology in 2d conformal gravity
- Quantisation of 2 + 1 gravity for g = 1 and g = 2
- Geometry and dynamics with time-dependent constraints
- Collective coordinates and BRST transformations or Gauge theories without gauge fields
- Geometry of fermionic constraints in superstring theories
- BRST and new superstring states
- Generalized canonical quantization of gauge theories with polarized second–class constraints
- Radiation field on superspace
- Participants
Dirac versus reduced phase space quantization
Published online by Cambridge University Press: 05 November 2011
- Frontmatter
- Contents
- The network
- Preface
- The constraint algebra of higher dimensional Chern-Simons theories
- Nonrelativistic Chern-Simons vortices from the constrained Hamiltonian formalism
- Classical solutions of gravitating Chern-Simons electrodynamics
- Exponentially localised instantons in a hierarchy of Higgs models
- Obstructions to ganging WZ terms: a symplectic curiosity
- Global aspects of symmetries in sigma models with torsion
- Canonical structure of the non-linear σ-model in a polynomial formulation
- A manifestly gauge-invariant approach to quantum theories of gauge fields
- On the Hamiltonian formulation of higher dimensional Chern-Simons gravity
- An Example of Loop Quantization
- Gauge fixing in constrained systems
- Light-cone formulation of gauge theories
- Hamiltonian constraints and Dirac observables
- Gauging kinematical and internal symmetry groups for extended systems
- On the harmonic interaction of three relativistic point particles
- Non existence of static multi-black-hole solutions in 2+1 dimensions
- Spherically symmetric gravity and the notion of time in general relativity
- Canonical decomposition of Belinskii-Zakharov one-soliton solutions
- Hamiltonian reduction and the R-matrix of the Calogero model
- Intrinsic approach to the Legendre transformation in super-mechanics
- Field-antifield description of anomalous theories
- Transfer matrix quantization of general relativity, and the problem of time
- The W3-particle
- Pure geometrical approach to singular Lagrangians with higher derivatives
- Dirac versus reduced phase space quantization
- Classical and quantum aspects of degenerate metric fields
- BRST-antibracket cohomology in 2d conformal gravity
- Quantisation of 2 + 1 gravity for g = 1 and g = 2
- Geometry and dynamics with time-dependent constraints
- Collective coordinates and BRST transformations or Gauge theories without gauge fields
- Geometry of fermionic constraints in superstring theories
- BRST and new superstring states
- Generalized canonical quantization of gauge theories with polarized second–class constraints
- Radiation field on superspace
- Participants
Summary
Abstract
The relationship between the Dirac and reduced phase space quantizations is investigated for spin models belonging to the class of Hamiltonian systems having no gauge conditions. It is traced out that the two quantization methods may give similar, or essentially different physical results, and, moreover, it is shown that there is a class of constrained systems, which can be quantized only by the Dirac method. A possible interpretation of the gauge degrees of freedom is given.
Introduction
There are two main methods to quantize the Hamiltonian systems with first class constraints: the Dirac quantization [1] and the reduced phase space quantization [2], whereas two other methods, the path integral method [3, 2] and the BRST quantization [4] being the most popular method for the covariant quantization of gauge-invariant systems, are based on and proceed from them [2, 5]. The basic idea of the Dirac method consists in imposing quantum mechanically the first class constraints as operator conditions on the states for singling out the physical ones [1]. The reduced phase space quantization first identifies the physical degrees of freedom at the classical level by the factorization of the constraint surface with respect to the action of the gauge group, generated by the constraints. Then the resulting Hamiltonian system is quantized as a usual unconstrained system [2]. Naturally, the problem of the relationship of these two methods arises. It was discussed in different contexts in literature [6], and there is an opinion that the differences between the two quantization methods can be traced out to a choice of factor ordering in the construction of various physical operators.
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- Geometry of Constrained Dynamical Systems , pp. 239 - 250Publisher: Cambridge University PressPrint publication year: 1995