The Application of Regge Calculus to Quantum Gravity and Quantum Field Theory in a Curved Background

Details The Application of Regge Calculus to Quantum Gravity and Quantum Field Theory in a Curved Background The Application of Regge Calculus to Quantum Gravity and Quantum Field Theory in a Curved Background

Oct 1982

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982rspsa.383..359w&link_type=abstract

Proceedings of The Royal Society of London. Series A, Mathematical and Physical Sciences, Volume 383, Issue 1785, pp. 359-377

Physics

15

Scientific paper

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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