Abstract
The use of Regge’s discrete formulation of classical general relativity in attempts at constructing a theory of simplicial quantum gravity is discussed briefly. Recent work on invariants of discretized three-manifolds, which provide a regularized version of the much earlier result of Ponzano and Regge, where the state sum was related to a Feynman path integral with the Regge action, has led to the search for invariants of discretized four-manifolds, which might be the basis for a four-dimensional theory of quantum gravity. This search is described, and recent developments in Regge calculus arising from it are outlined. This paper is based on a talk given at the LMS Durham Symposium on Quantum Concepts in Space and Time, July 1994.
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