Midi-superspace Models of Canonical Quantum Gravity

Abstract

A midi-superspace model is a field theory obtained by symmetry reduction of a parent gravitational theory. Such models have proven useful for exploring the classical and quantum dynamics of the gravitational field. I present 3 recent classes of results pertinent to canonical quantization of vacuum general relativity in the context of midi-superspace models. (1) I give necessary and sufficient conditions such that a given symmetry reduction can be performed at the level of the Lagrangian or Hamiltonian. (2) I discuss the Hamiltonian formulation of models based upon cylindrical and toroidal symmetry. In particular, I explain how these models can be identified with parametrized field theories of wave maps, thus a natural strategy for canonical quantization is available. (3) The quantization of a parametrized field theory, such as the midi-superspace models considered in (2), requires construction of a quantum field theory on a fixed (flat) spacetime that allows for time evolution along arbitrary foliations of spacetime. I discuss some recent results on the possibility of finding such a quantum field theory.

29 pages, RevTex, contribution to "Quantum Gravity in the Southern Cone II", Bariloche, Argentina, January 6-10, 1998

References in corpus (2)

• Canonical quantization of cylindrical gravitational waves with two polarizations
• Energy and directional signatures for plane quantized gravity waves

Cited by in corpus (23)

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• Quantization of Midisuperspace Models
• Quantum Gowdy $T^3$ Model: Schrodinger Representation with Unitary Dynamics
• Feasibility of a Unitary Quantum Dynamics in the Gowdy $T^3$ Cosmological Model
• Mathematical Structure of Loop Quantum Cosmology: Homogeneous Models
• On Unitary Time Evolution in Gowdy $T^3$ Cosmologies
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• Symmetry reduction of gravitational Lagrangians
• Gauge fixing and the Hamiltonian for cylindrical spacetimes
• Nonlinear quantum gravity on the constant mean curvature foliation
• Quantum cosmology of pure connection general relativity
• Minisuperspace models of discrete systems
• Towards conformal loop quantum gravity
• Infrared signatures of quantum bounce in a minisuperspace analysis of Lema\^ıtre-Tolman-Bondi dust collapse
• Testing general covariance in effective models motivated by Loop Quantum Gravity
• Midisuperspace quantization: possibilities for fractional and emergent spacetime dimensions
• Gravitational dynamics in a 2+1+1 decomposed spacetime along nonorthogonal double foliations: Hamiltonian evolution and gauge fixing
• Black holes and Rindler superspace: classical singularity and quantum unitarity