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

C Meusburger·B J Schroers
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Abstract

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 Poincaré 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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C Meusburger, B J Schroers. 2005-05-16. Boundary conditions and symplectic structure in the Chern-Simons formulation of (2+1)-dimensional gravity. https://doi.org/10.1088/0264-9381%2F22%2F17%2F021

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