A lattice quantum gravity model with surfacelike excitations in 4dimensional spacetime
Abstract
A lattice quantum gravity model in 4 dimensional Riemannian spacetime is constructed based on the SU(2) Ashtekar formulation of general relativity. This model can be understood as one of the family of models sometimes called ``spin foam models.'' A version of the action of general relativity in continuum is introduced and its lattice version is defined. A dimensionless ``(inverse) coupling'' constant is defined so that the value of the action of the model is finite per lattice point. The path integral of the model is expanded in the characters and shown to be written as a sum over surfacelike excitations in spacetime. A 3 dimensional version of the model exists and can be reduced to lattice BF theory. The expectation values of some quantities are computed in 3 dimensions and the meanings of the results are discussed. Although the model is studied on a hyper cubic lattice for simplicity, it can be generalized to a randomly triangulated lattice with small modifications.
 Publication:

arXiv eprints
 Pub Date:
 June 2000
 arXiv:
 arXiv:grqc/0006088
 Bibcode:
 2000gr.qc.....6088I
 Keywords:

 General Relativity and Quantum Cosmology
 EPrint:
 Latex, 17 pages, No figure