Quantization of 2+1 Gravity on the Torus
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We use the polygon representation of 2+1--dimensional gravity to explicitly carry out the canonical quantization of a universe with the topology of a torus. The mapping-class-invariant wave function for a quantum ''big bounce'', is reminiscent of the interference patterns of linear gratings. We consider the ``problem of time'' of quantum gravity: for one choice of internal time the universe recovers a semiclassical interpretation after the bounce, with a wave packet centered at a single geometry; for another choice of internal time, the quantum solutions involve interference between macroscopically distinct universes.
TeX file, 11 pages, proceedings of the CAP 95 meeting in Quebec
TeX file, 11 pages, proceedings of the CAP 95 meeting in Quebec