Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1997-06-26
Int.J.Mod.Phys. A13 (1998) 4023-4048
Physics
High Energy Physics
High Energy Physics - Theory
Latex file, 26 pages, no figures
Scientific paper
10.1142/S0217751X98001888
The usual description of 2+1 dimensional Einstein gravity as a Chern-Simons (CS) theory is extended to a one parameter family of descriptions of 2+1 Einstein gravity. This is done by replacing the Poincare' gauge group symmetry by a q-deformed Poincare' gauge group symmetry, with the former recovered when q-> 1. As a result, we obtain a one parameter family of Hamiltonian formulations for 2+1 gravity. Although formulated in terms of noncommuting dreibeins and spin-connection fields, our expression for the action and our field equations, appropriately ordered, are identical in form to the ordinary ones. Moreover, starting with a properly defined metric tensor, the usual metric theory can be built; the Christoffel symbols and space-time curvature having the usual expressions in terms of the metric tensor, and being represented by c-numbers. In this article, we also couple the theory to particle sources, and find that these sources carry exotic angular momentum. Finally, problems related to the introduction of a cosmological constant are discussed.
Bimonte Giuseppe
Musto Renato
Stern Ady
Vitale Patrizia
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