English

Multi-plaquette solutions for discretized Ashtekar gravity

General Relativity and Quantum Cosmology 2009-10-28 v2

Abstract

A discretized version of canonical quantum gravity proposed by Loll is investigated. After slightly modifying Loll's discretized Hamiltonian constraint, we encode its action on the spin network states in terms of combinatorial topological manipulations of the lattice loops. Using this topological formulation we find new solutions to the discretized Wheeler-Dewitt equation. These solutions have their support on the connected set of plaquettes. We also show that these solutions are not normalizable with respect to the induced heat-kernel measure on SL(2,C)SL(2,{\bf C}) gauge theories.

Keywords

Cite

@article{arxiv.gr-qc/9510019,
  title  = {Multi-plaquette solutions for discretized Ashtekar gravity},
  author = {Kiyoshi Ezawa},
  journal= {arXiv preprint arXiv:gr-qc/9510019},
  year   = {2009}
}

Comments

11 pages Latex (2 figures available as a postscript file, the rough discussion on the non-normalizability has been made exact. )

R2 v1 2026-07-22T12:50:41.668Z