Feynman Rules for Simplicial Gravity

Abstract

We develop the general formalism for performing perturbative diagrammatic expansions in the lattice theory of quantum gravity. The results help establish a precise correspondence between continuum and lattice quantities, and should be a useful guide for non-perturbative studies of gravity. The Feynman rules for Regge's simplicial lattice formulation of gravity are then discussed in detail in two dimensions. As an application, the two-dimensional conformal anomaly due to a $D$-component scalar field is explicitly computed in perturbation theory.