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Compact phase space, cosmological constant, discrete time
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Compact phase space, cosmological constant, discrete time
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We study the quantization of geometry in the presence of a cosmological constant, using a discretiza- tion with constant-curvature simplices. Phase space turns out to be compact and the Hilbert space finite dimensional for each link. Not only the intrinsic, but also the extrinsic geometry turns out to be discrete, pointing to discreetness of time, in addition to space. We work in 2+1 dimensions, but these results may be relevant also for the physical 3+1 case.
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Cited by 1 Pith paper
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Polymer quantum mechanics on compact configuration spaces
Polymer quantization on compact spaces yields finite graph Hilbert spaces whose exact ring and box spectra recover Schrödinger QM as lattice spacing vanishes.
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