Topological Lattice Gravity Using Self-Dual Variables

Details Topological Lattice Gravity Using Self-Dual Variables Topological Lattice Gravity Using Self-Dual Variables

1996-03-20

arxiv.org/abs/gr-qc/9603030v1

Class.Quant.Grav.13:2617-2634,1996

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

22 pages, revtex, no figures

Scientific paper

10.1088/0264-9381/13/10/003

Topological gravity is the reduction of general relativity to flat space-times. A lattice model describing topological gravity is developed starting from a Hamiltonian lattice version of $B\w F$ theory. The extra symmetries not present in gravity that kill the local degrees of freedom in $B\wedge F$ theory are removed. The remaining symmetries preserve the geometrical character of the lattice. Using self-dual variables, the conditions that guarantee the geometricity of the lattice become reality conditions. The local part of the remaining symmetry generators, that respect the geometricity-reality conditions, has the form of Ashtekar's constraints for GR. Only after constraining the initial data to flat lattices and considering the non-local (plus local) part of the constraints does the algebra of the symmetry generators close. A strategy to extend the model for non-flat connections and quantization are discussed.

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