Combinatorial quantization of Euclidean gravity in three dimensions

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In the Chern-Simons formulation of Einstein gravity in 2+1 dimensions, the phase space is the moduli space of flat G-connections on a two-dimensional surface, where G is a typically non-compact Lie group which depends on the signature of space-time and the cosmological constant. For Euclidean signature and vanishing cosmological constant, G is the three-dimensional Euclidean group. For this case the Poisson structure of the moduli space is given explicitly in terms of a classical r-matrix. It is shown that the quantum R-matrix of the quantum double D(SU(2)) provides a quantization of that Poisson structure.

Original languageEnglish
Title of host publicationQuantization of Singular Symplectic Quotients
EditorsN. P. Landsman, M. Pflaum, M. Schlichenmaier
PublisherBirkhäuser
Pages307-327
Number of pages21
ISBN (Electronic)978-3-0348-8364-1
ISBN (Print)978-3-0348-9535-4
DOIs
Publication statusPublished - 2001
EventWorkshop on Quantization of Singular Symplectic Quotients 1999 - Oberwolfach, Germany
Duration: 2 Aug 19996 Aug 1999

Publication series

NameProgress in Mathematics
PublisherBirkhäuser Basel
Volume198
ISSN (Print)0743-1643

Conference

ConferenceWorkshop on Quantization of Singular Symplectic Quotients 1999
CountryGermany
CityOberwolfach
Period2/08/996/08/99

Keywords

  • CHERN-SIMONS THEORY
  • QUANTUM

Cite this

Schroers, B. J. (2001). Combinatorial quantization of Euclidean gravity in three dimensions. In N. P. Landsman, M. Pflaum, & M. Schlichenmaier (Eds.), Quantization of Singular Symplectic Quotients (pp. 307-327). (Progress in Mathematics; Vol. 198). Birkhäuser. https://doi.org/10.1007/978-3-0348-8364-1_12