Finite quantum gravity in locally conformally flat spacetime through covariant spectral regularization
Abstract
Pure gravity quantum gravity (pure gravity QG) is non-renormalizable at two and higher loop level. One of the main characteristics of objects occurring in QG is their Lorentz covariance. QG necessitates the analysis of a collection of Lorentz covariant terms of higher and higher order, which is not feasible using renormailization. This paper describes how the regularization technique known as covariant spectral regularization (CSR) can be used to analyze Lorentz covariant 4-tensor valued measures on Minkowski space. The graviton vacuum polarization tensor is cast as such a measure and CSR is used to obtain a well defined and finite function representing this tensor. This is then used to compute the Feynman amplitudes for examples of one-loop, two-loop and n-loop graviton-graviton scattering in pure gravity QG. The CSR method results in functions (densities) representing divergent Feynman integrals without requiring renormalization or counterterms. Therefore it can be used to analyze arbitrarily complicated multiloop QG Feynman diagrams without being crippled by a proliferation of counterterms, as is classical QG.
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BibTeX
@misc{mashford2026finite,
title = {{Finite quantum gravity in locally conformally flat spacetime through covariant spectral regularization}},
author = {John Mashford},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.23924},
eprint = {2610.23924},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.23924},
}
RIS
TY - UNPB
TI - Finite quantum gravity in locally conformally flat spacetime through covariant spectral regularization
AU - John Mashford
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.23924
UR - https://arxiv.org/abs/2610.23924
AB - Pure gravity quantum gravity (pure gravity QG) is non-renormalizable at two and higher loop level. One of the main characteristics of objects occurring in QG is their Lorentz covariance. QG necessitates the analysis of a collection of Lorentz covariant terms of higher and higher order, which is not feasible using renormailization. This paper describes how the regularization technique known as covariant spectral regularization (CSR) can be used to analyze Lorentz covariant 4-tensor valued measures on Minkowski space. The graviton vacuum polarization tensor is cast as such a measure and CSR is used to obtain a well defined and finite function representing this tensor. This is then used to compute the Feynman amplitudes for examples of one-loop, two-loop and n-loop graviton-graviton scattering in pure gravity QG. The CSR method results in functions (densities) representing divergent Feynman integrals without requiring renormalization or counterterms. Therefore it can be used to analyze arbitrarily complicated multiloop QG Feynman diagrams without being crippled by a proliferation of counterterms, as is classical QG.
ER -