Boundary conditions and symplectic structure in the Chern-Simons formulation of (2+1)-dimensional gravity

Details Boundary conditions and symplectic structure in the Chern-Simons formulation of (2+1)-dimensional gravity Boundary conditions and symplectic structure in the Chern-Simons formulation of (2+1)-dimensional gravity

2005-05-16

arxiv.org/abs/gr-qc/0505071v1

Class.Quant.Grav. 22 (2005) 3689-3724

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

44 pages, 3 eps figures

Scientific paper

10.1088/0264-9381/22/17/021

We propose a description of open universes in the Chern-Simons formulation of (2+1)-dimensional gravity where spatial infinity is implemented as a puncture. At this puncture, additional variables are introduced which lie in the cotangent bundle of the Poincar\'e group, and coupled minimally to the Chern-Simons gauge field. We apply this description of spatial infinity to open universes of general genus and with an arbitrary number of massive spinning particles. Using results of [9] we give a finite dimensional description of the phase space and determine its symplectic structure. In the special case of a genus zero universe with spinless particles, we compare our result to the symplectic structure computed by Matschull in the metric formulation of (2+1)-dimensional gravity. We comment on the quantisation of the phase space and derive a quantisation condition for the total mass and spin of an open universe.

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