Abstract
The application of Regge calculus to quantum gravity and quantum field theory in a curved background is discussed. A discrete form of exterior differential calculus is developed, and this is used to obtain Laplacians for P -forms on the Regge manifold. To assess the accuracy of these approximations, the eigenvalues of the discrete Laplacians were calculated for the regular tesselations of S 2 and S 3 . The results indicate that the methods obtained in this paper may be used in curved space–times with an accuracy comparing with that obtained in lattice gauge theories on a flat background. It also becomes evident that Regge calculus provides particularly suitable lattices for Monte-Carlo techniques.
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