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arXiv · 0903.4809

A Quantum Goldman Bracket for Loops on Surfaces

J. E. Nelson·R. F. Picken
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Abstract

In the context of (2+1)--dimensional gravity, we use holonomies of constant connections which generate a $q$--deformed representation of the fundamental group to derive signed area phases which relate the quantum matrices assigned to homotopic loops. We use these features to determine a quantum Goldman bracket (commutator) for intersecting loops on surfaces, and discuss the resulting quantum geometry.

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J. E. Nelson, R. F. Picken. 2009-03-27. A Quantum Goldman Bracket for Loops on Surfaces. https://doi.org/10.1142/s0217751x09046199

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