Finite One-Loop Calculations in Quantum Gravity: Graviton Self-Energy, Perturbative Gauge Invariance and Slavnov-Ward Identities

Abstract

In this paper we show that the one-loop graviton self-energy contribution is ultraviolet finite, without introducing counterterms, and cutoff-free in the framework of causal perturbation theory. In addition, it satisfies the gravitational Slavnov-Ward identities for the two-point connected Green function. The condition of perturbative gauge invariance to second order for loop graphs is proved. Corrections to the Newtonian potential are also derived.