A Quantum Goldman Bracket for Loops on Surfaces

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.

Invited talk (J. E. Nelson) at II Workshop on Quantum Gravity and Noncommutative Geometry, Univ. Lusofona, Lisbon, September 2008. 18 pages, 24 figures

References in corpus (3)

• Quantum Holonomies in (2+1)-Dimensional Gravity
• Quantum Matrix Pairs
• Parametrization of the moduli space of flat SL(2,R) connections on the torus

Cited by in corpus (1)

• Lambda Models From Chern-Simons Theories