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Midi-superspace Models of Canonical Quantum Gravity | | C. G. Torre
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30 Jun 1998 | | Journal: | Int.J.Theor.Phys. 38 (1999) 1081-1102 | | Subject: | gr-qc hep-th | | Affiliation: | Utah State University | | 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. | | Source: | arXiv, gr-qc/9806122 | | Services: | Forum | Review | PDF | Favorites | |
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