A Quantum Goldman Bracket for Loops on Surfaces

Details A Quantum Goldman Bracket for Loops on Surfaces A Quantum Goldman Bracket for Loops on Surfaces

2009-03-27

arxiv.org/abs/0903.4809v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Invited talk (J. E. Nelson) at II Workshop on Quantum Gravity and Noncommutative Geometry, Univ. Lusofona, Lisbon, September 2

Scientific paper

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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