Topological lattice gravity using selfdual variables
Mar, 199622 pages
Published in:
- Class.Quant.Grav. 13 (1996) 2617-2634
e-Print:
- gr-qc/9603030 [gr-qc]
Report number:
- CGPG-96-3-3
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Abstract: (arXiv)
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 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.- quantum gravity
- gravitation: topological
- lattice field theory: constraint
- Hamiltonian formalism
- duality
- group theory: SO(3,1)
- quantization
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