C Meusburger and B J Schroers 2003 Class. Quantum Grav. 20 2193 doi:10.1088/0264-9381/20/11/318
C Meusburger and B J Schroers
Show affiliationsIn the formulation of (2 + 1)-dimensional gravity as a Chern–Simons gauge theory, the phase space is the moduli space of flat Poincaré group connections. Using the combinatorial approach developed by Fock and Rosly, we give an explicit description of the phase space and its Poisson structure for the general case of a genus g oriented surface with punctures representing particles and a boundary playing the role of spatial infinity. We give a physical interpretation and explain how the degrees of freedom associated with each handle and each particle can be decoupled. The symmetry group of the theory combines an action of the mapping class group with asymptotic Poincaré transformations in a nontrivial fashion. We derive the conserved quantities associated with the latter and show that the mapping class group of the surface acts on the phase space via Poisson isomorphisms.
81T13 Yang-Mills and other gauge theories (See also 53C07, 58E15)
83C45 Quantization of the gravitational field
83C05 Einstein's equations (general structure, canonical formalism, Cauchy problems)
Issue 11 (7 June 2003)
Received 30 January 2003
Published 8 May 2003
C Meusburger and B J Schroers 2003 Class. Quantum Grav. 20 2193
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