A New Discretization of Classical and Quantum General Relativity
General Relativity and Quantum Cosmology
2008-02-03 v2 High Energy Physics - Lattice
High Energy Physics - Theory
Abstract
We propose a new discrete approximation to the Einstein equations, based on the Capovilla-Dell-Jacobson form of the action for the Ashtekar variables. This formulation is analogous to the Regge calculus in that the curvature has support on sets of measure zero. Both a Lagrangian and Hamiltonian formulation are proposed and we report partial results about the constraint algebra of the Hamiltonian formulation. We find that the discrete versions of the diffeomorphism constraints do not commute with each other or with the Hamiltonian constraint.
Cite
@article{arxiv.gr-qc/9304005,
title = {A New Discretization of Classical and Quantum General Relativity},
author = {O. Bostrom and M. Miller and L. Smolin},
journal= {arXiv preprint arXiv:gr-qc/9304005},
year = {2008}
}
Comments
25 pages, LaTeX (calculational errors corrected, revised conclusions)