Topological lattice gravity using selfdual variables

Mar, 1996
22 pages
Published in:
  • Class.Quant.Grav. 13 (1996) 2617-2634
e-Print:
Report number:
  • CGPG-96-3-3

Citations per year

1996200220082014202001234
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 BFB\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.
  • quantum gravity
  • gravitation: topological
  • lattice field theory: constraint
  • Hamiltonian formalism
  • duality
  • group theory: SO(3,1)
  • quantization