All Physics Faculty Publications

Document Type

Article

Journal/Book Title/Conference

Physical Review D

Volume

53

Issue

10

Publisher

American Physical Society

Publication Date

1996

First Page

5634

Last Page

5650

DOI

10.1103/PhysRevD.53.5634

Abstract

The Hamiltonian structure of spacetimes with two commuting Killing vector fields is analyzed for the purpose of addressing the various problems of time that arise in canonical gravity. Two specific models are considered: (i) cylindrically symmetric spacetimes, and (ii) toroidally symmetric spacetimes, which respectively involve open and closed universe boundary conditions. For each model canonical variables which can be used to identify points of space and instants of time, {\it i.e.}, internally defined spacetime coordinates, are identified. To do this it is necessary to extend the usual ADM phase space by a finite number of degrees of freedom. Canonical transformations are exhibited that identify each of these models with harmonic maps in the parametrized field theory formalism. The identifications made between the gravitational models and harmonic map field theories are completely gauge invariant, that is, no coordinate conditions are needed. The degree to which the problems of time are resolved in these models is discussed.

Comments

Originally published by the American Physical Society. Publisher's PDF can be accessed through Physical Review D - Particles, Fields, Gravitation, and Cosmology. Note: Joseph Romano is currently at University of Texas at Brownsville.

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