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Quantum Holonomies in (2+1)-Dimensional Gravity

J. E. Nelson·R. F. Picken
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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.

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J. E. Nelson, R. F. Picken. 1999-11-03. Quantum Holonomies in (2+1)-Dimensional Gravity. https://doi.org/10.1016/s0370-2693(99)01407-0

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