Scalar Matter Coupled to Quantum Gravity in the Causal Approach: One-Loop Calculations and Perturbative Gauge Invariance

Abstract

Quantum gravity coupled to scalar massive matter fields is investigated in the framework of causal perturbation theory using the Epstein–Glaser regularization/renormalization scheme. Detailed one-loop calculations include the matter loop graviton self-energy and the matter self-energy. The condition of perturbative operator gauge invariance to second order implies the usual Slavnov–Ward identities for the graviton two-point connected Green function in the loop graph sector and generates the correct quartic graviton-matter interaction in the tree graph sector. The mass zero case is also discussed.