All Physics Faculty Publications

Document Type

Article

Journal/Book Title/Conference

International Journal of Theoretical Physics

Volume

38

Issue

4

Publisher

Springer Verlag

Publication Date

1999

First Page

1081

Last Page

1102

DOI

10.1023/A:1026650212053

Abstract

A midisuperspace 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 three recent classes of results pertinent to canonical quantization of vacuum general relativity in the context of midisuperspace 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 midisuperspace 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.

Comments

Originally published by Springer Verlag. Publisher's PDF can be accessed through the International Journal of Theoretical Physics. Article is also available through arXiv.org.

http://arxiv.org/abs/gr-qc/9806122

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