Constant connections, quantum holonomies and the Goldman bracket
Mathematical Physics
2007-05-23 v3 General Relativity and Quantum Cosmology
High Energy Physics - Theory
math.MP
Abstract
In the context of (2+1)--dimensional quantum gravity with negative cosmological constant and topology R x T^2, constant matrix--valued connections generate a q--deformed representation of the fundamental group, and signed area phases relate the quantum matrices assigned to homotopic loops. Some features of the resulting quantum geometry are explored, and as a consequence a quantum version of the Goldman bracket is obtained
Cite
@article{arxiv.math-ph/0412007,
title = {Constant connections, quantum holonomies and the Goldman bracket},
author = {J. E. Nelson and R. F. Picken},
journal= {arXiv preprint arXiv:math-ph/0412007},
year = {2007}
}
Comments
25 pages, 43 figures, using ATMP style file, to appear Adv.Theor.Math.Phys. Vol 9 (2005)