GAUGE FIXING AND QUANTUM GROUP SYMMETRIES IN (2+1)-GRAVITY

被引：0

作者：

Meusburger, Catherine ^{[1
]}

Schoenfeld, Torsten ^{[1
]}

机构：

[1] Univ Erlangen Nurnberg, Dept Math, D-91058 Erlangen, Germany

来源：

INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS | 2013年 / 10卷 / 08期

关键词：

Chern-Simons theory; gauge fixing; dynamical r-matrix; CHERN-SIMONS THEORY; COMBINATORIAL QUANTIZATION; GRAVITY; GEOMETRY; SPACE;

D O I：

10.1142/S0219887813600049

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We summarize the results obtained by applying Dirac's gauge fixing formalism to the combinatorial description of the Chern-Simons formulation of (2+1)-gravity and their implications for the symmetries of the quantum theory. While the combinatorial description of the phase space exhibits standard Poisson-Lie symmetries, every gauge fixing condition based on two point particles yields a Poisson structure determined by a dynamical classical r-matrix. By considering transformations between different gauge fixing conditions, it is possible to classify all gauge fixed Poisson structures in terms of two standard solutions of the dynamical classical Yang-Baxter equation. We discuss the conclusions that can be drawn from this about the symmetries of (2+1)-dimensional quantum gravity.

引用

页数：13

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