Classical and quantum geometry of moduli spaces in three-dimensional gravity
Mathematical Physics
2007-05-23 v1 math.MP
Abstract
We describe some results concerning the phase space of 3-dimensional Einstein gravity when space is a torus and with negative cosmological constant. The approach uses the holonomy matrices of flat SL(2,R) connections on the torus to parametrise the geometry. After quantization, these matrices acquire non-commuting entries, in such a way that they satisfy q-commutation relations and exhibit interesting geometrical properties. In particular they lead to a quantization of the Goldman bracket.
Cite
@article{arxiv.math-ph/0501051,
title = {Classical and quantum geometry of moduli spaces in three-dimensional gravity},
author = {J. E. Nelson and R. F. Picken},
journal= {arXiv preprint arXiv:math-ph/0501051},
year = {2007}
}
Comments
12 pages, including contents page (proceedings format), submitted to the Proceedings of the XIII Fall Workshop on Geometry and Physics, Murcia, Sept. 20-22, 2004