A Quantum Goldman Bracket for Loops on Surfaces
General Relativity and Quantum Cosmology
2015-05-13 v1 High Energy Physics - Theory
Mathematical Physics
math.MP
Abstract
In the context of (2+1)--dimensional gravity, we use holonomies of constant connections which generate a --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.
Cite
@article{arxiv.0903.4809,
title = {A Quantum Goldman Bracket for Loops on Surfaces},
author = {J. E. Nelson and R. F. Picken},
journal= {arXiv preprint arXiv:0903.4809},
year = {2015}
}
Comments
Invited talk (J. E. Nelson) at II Workshop on Quantum Gravity and Noncommutative Geometry, Univ. Lusofona, Lisbon, September 2008. 18 pages, 24 figures