One-loop beta-functions for renormalisable gravity

TL;DR

This paper calculates the one-loop beta-functions for renormalisable quantum gravity coupled with scalars, clarifying previous discrepancies between coordinate and momentum space methods and extending insights to fermions.

Contribution

It introduces a coordinate space approach with Schwinger De Witt technique to accurately compute beta-functions, resolving prior inconsistencies in quantum gravity calculations.

Findings

Resolved contradictions between coordinate and momentum space calculations.

Extended the methodology to include fermions in quantum gravity.

Provided consistent beta-functions for renormalisable gravity with scalars.

Abstract

We compute the one-loop beta-functions for renormalisable quantum gravity coupled to scalars using the co-ordinate space approach and generalised Schwinger De Witt technique. We resolve apparent contradictions with the corresponding momentum space calculations, and indicate how our results also resolve similar inconsistencies in the fermion case.