Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1997-11-17
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
50 pages latex. 8 postscript figures. Uses psfig.sty
Scientific paper
A lattice model for four dimensional Euclidean quantum general relativity is proposed for a simplicial spacetime. It is shown how this model can be expressed in terms of a sum over worldsheets of spin networks, and an interpretation of these worldsheets as spacetime geometries is given, based on the geometry defined by spin networks in canonical loop quantized GR. The spacetime geometry has a Planck scale discreteness which arises "naturally" from the discrete spectrum of spins of SU(2) representations (and not from the use of a spacetime lattice). The lattice model of the dynamics is a formal quantization of the classical lattice model of \cite{Rei97a}, which reproduces, in a continuum limit, Euclidean general relativity.
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