On the power counting of loop diagrams in general relativity

TL;DR

This paper demonstrates that apparent divergences in loop diagrams in general relativity are gauge artifacts, and proper power counting reveals a well-behaved energy expansion for quantum effects.

Contribution

It shows that cancellations in loop diagrams restore the expected energy expansion behavior, clarifying the role of gauge choices in quantum gravity calculations.

Findings

Cancellations occur in specific loop diagrams.

Apparent divergences are gauge artifacts.

Quantum loops have a well-behaved energy expansion.

Abstract

A class of loop diagrams in general relativity appears to have a behavior which would upset the utility of the energy expansion for quantum effects. We show through the study of specific diagrams that cancellations occur which restore the expected behaviour of the energy expansion. By considering the power counting in a physical gauge we show that the apparent bad behavior is a gauge artifact, and that the quantum loops enter with a well behaved energy expansion.