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
Classical and quantum aspects of degenerate metric fields
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
Degenerate space-time metrics are discussed in the framework of gravitation in interaction with scalar fields. Minisuperspace quantisations are effected leading to coherent states that exhibit enhanced fluctuations in the vicinity of classical cosmological loci. An alternative approach for implementing the Hamiltonian constraint is offered in terms of a spinor state space and an analysis of solutions to the scalar field equation on a 2-dimensional topologically non-trivial manifold with a degenerate metric is summarised.
Introduction
In the absence of a viable quantum description of the gravitational field attention is sometimes directed to the so called “mini-superspace” models [1] in which all but a small number of degrees of freedom of the gravitational field are suppressed and the dynamics is reduced from field theory to quantum mechanics. Such a programme is fraught with both conceptual and technical difficulties. It ignores many effects that may be of relevance in determining a viable quantum description. One restricts to quantum states describing highly symmetric geometries that possess a preferred class of spacelike foliations that may be used to order temporal phenomena in a classical spacetime. Even within this restricted framework there is no preferred way to effect a quantisation of Einstein's equations of motion tensorial nature of these equations gives rise to a constrained canonical system and there is no known criterion that singles out a particular mapping from the classical constraints to a set of quantum operators on a Hilbert space.
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- Chapter
- Information
- Geometry of Constrained Dynamical Systems , pp. 251 - 263Publisher: Cambridge University PressPrint publication year: 1995