Unitary Equivalence of the Metric and Holonomy Formulations of 2+1 Dimensional Quantum Gravity on the Torus

Preprint

31 December 1992

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.gr-qc/9210007

Abstract

Recent work on canonical transformations in quantum mechanics is applied to transform between the Moncrief metric formulation and the Witten-Carlip holonomy formulation of 2+1-dimensional quantum gravity on the torus. A non-polynomial factor ordering of the classical canonical transformation between the metric and holonomy variables is constructed which preserves their classical modular transformation properties. An extension of the definition of a unitary transformation is briefly discussed and is used to find the inner product in the holonomy variables which makes the canonical transformation unitary. This defines the Hilbert space in the Witten-Carlip formulation which is unitarily equivalent to the natural Hilbert space in the Moncrief formulation. In addition, gravitational theta-states arising from ``large'' diffeomorphisms are found in the theory.

Keywords

All Related Versions

Version 1, 1992-10-13, ArXiv
Version 2, 1992-12-31, ArXiv
Published version: Physical Review D, 47 (10), 4458.

This publication has 0 references indexed in Scilit: