Remarks on the Reduced Phase Space of (2+1)-Dimensional Gravity on a Torus in the Ashtekar Formulation

Details Remarks on the Reduced Phase Space of (2+1)-Dimensional Gravity on a Torus in the Ashtekar Formulation Remarks on the Reduced Phase Space of (2+1)-Dimensional Gravity on a Torus in the Ashtekar Formulation

1997-12-02

arxiv.org/abs/gr-qc/9712011v3

Class.Quant.Grav.15:3031-3039,1998

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

13 pages, Latex. More details have been included and the expression for the finite residual gauge transformations has been wor

Scientific paper

10.1088/0264-9381/15/10/009

We examine the reduced phase space of the Barbero-Varadarajan solutions of the Ashtekar formulation of (2+1)-dimensional general relativity on a torus. We show that it is a finite-dimensional space due to existence of an infinite dimensional residual gauge invariance which reduces the infinite-dimensional space of solutions to a finite-dimensional space of gauge-inequivalent solutions. This is in agreement with general arguments which imply that the number of physical degrees of freedom for (2+1)-dimensional Ashtekar gravity on a torus is finite.

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