Quantum Holonomies in (2+1)-Dimensional Gravity

Abstract

We describe an approach to the quantisation of (2+1)-dimensional gravity with topology R x T^2 and negative cosmological constant, which uses two quantum holonomy matrices satisfying a q-commutation relation. Solutions of diagonal and upper-triangular form are constructed, which in the latter case exhibit additional, non-trivial internal relations for each holonomy matrix. Representations are constructed and a group of transformations - a quasi-modular group - which preserves this structure, is presented.

10 pages Latex no figures

References in corpus (1)

• The Quantum Modular Group in (2+1)-Dimensional Gravity

Cited by in corpus (7)

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• Quantum geometry from 2+1 AdS quantum gravity on the torus
• A quantum Goldman bracket in 2+1 quantum gravity
• A Quantum Goldman Bracket for Loops on Surfaces
• Quantum Holonomies and the Heisenberg Group