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

TL;DR

This paper demonstrates that one-loop graviton self-energy calculations are ultraviolet finite and gauge invariant within causal perturbation theory, providing new insights into quantum gravity and corrections to Newtonian potential.

Contribution

It shows the ultraviolet finiteness and gauge invariance of one-loop graviton self-energy without counterterms, advancing quantum gravity calculations.

Findings

Ultraviolet finiteness of graviton self-energy

Satisfaction of Slavnov-Ward identities

Perturbative gauge invariance proven to second order

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.