Quantum Holonomies in (2+1)-Dimensional Gravity

Details Quantum Holonomies in (2+1)-Dimensional Gravity Quantum Holonomies in (2+1)-Dimensional Gravity

1999-11-02

arxiv.org/abs/gr-qc/9911005v2

Phys.Lett. B471 (2000) 367-372

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

10 pages Latex no figures

Scientific paper

10.1016/S0370-2693(99)01407-0

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.

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