On diffeomorphism invariance for lattice theories

Details On diffeomorphism invariance for lattice theories On diffeomorphism invariance for lattice theories

1996-11-13

arxiv.org/abs/gr-qc/9611034v1

Nucl.Phys. B493 (1997) 475-490

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

11 Pages, Revtex, 3 figures

Scientific paper

10.1016/S0550-3213(97)00141-7

We consider the role of the diffeomorphism constraint in the quantization of lattice formulations of diffeomorphism invariant theories of connections. It has been argued that in working with abstract lattices, one automatically takes care of the diffeomorphism constraint in the quantum theory. We use two systems in order to show that imposing the diffeomorphism constraint is imperative to obtain a physically acceptable quantum theory. First, we consider $2+1$ gravity where an exact lattice formulation is available. Next, general theories of connections for compact gauge groups are treated, where the quantum theories are known --for both the continuum and the lattice-- and can be compared.

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