Gauge fixing in (2+1)-gravity: Dirac bracket and spacetime geometry

Abstract

We consider (2+1)-gravity with vanishing cosmological constant as a constrained dynamical system. By applying Dirac's gauge fixing procedure, we implement the constraints and determine the Dirac bracket on the gauge-invariant phase space. The chosen gauge fixing conditions have a natural physical interpretation and specify an observer in the spacetime. We derive explicit expressions for the resulting Dirac brackets and discuss their geometrical interpretation. In particular, we show that specifying an observer with respect to two point particles gives rise to conical spacetimes, whose deficit angle and time shift are determined, respectively, by the relative velocity and minimal distance of the two particles.

44 pages, 7 figures; v2 makes a few small improvements suggested by referees

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Cited by in corpus (6)

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• Coisotropic Lie bialgebras and complementary dual Poisson homogeneous spaces
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• Quantum groups and noncommutative spacetimes with cosmological constant
• Darboux families and the classification of real four-dimensional indecomposable coboundary Lie bialgebras
• Scalar Product for a Version of Minisuperspace Model with Grassmann Variables