A New Discretization of Classical and Quantum General Relativity

Details A New Discretization of Classical and Quantum General Relativity A New Discretization of Classical and Quantum General Relativity

1993-04-05

arxiv.org/abs/gr-qc/9304005v2

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

25 pages, LaTeX (calculational errors corrected, revised conclusions)

Scientific paper

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.

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