2005/01/20 by J. E. Nelson, Nelson, J. E., Roger Picken +2
Mathematics · Physics and Astronomy · #83C45 #Advanced Operator Algebra Research #Black Holes and Theoretical Physics #FOS: Physical sciences #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #math-ph #math.MP #msc:83C45
paper · pdf · doi:10.48550/arxiv.math-ph/0501051
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
arxiv created 2005/01/20 · openalex publication_date 2005/01/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.