Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1993-05-27
Phys.Rev.D49:1684-1688,1994
Physics
High Energy Physics
High Energy Physics - Theory
11 pages, CTP # 2210, Plain TeX
Scientific paper
10.1103/PhysRevD.49.1684
We investigate the canonical quantization of gravity coupled to pointlike matter in 2+1 dimensions. Starting from the usual point particle action in the first order formalism, we introduce auxiliary variables which make the action locally Poincar\'e invariant. A Hamiltonian analysis shows that the gauge group is actually larger than the Poincar\'e group -- certain additional gauge constraints are present which act on the matter degrees of freedom. These additional constraints are necessary to mimic the diffeomorphism invariance present if the theory is formulated with a spacetime metric. The additional gauge constraints are realized projectively in the quantum theory, with a phase in the composition law for finite gauge transformations. That phase is responsible for the braid invariance of physical observables (holonomies).
Kabat Daniel
Ortiz Miguel
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