Dimensional Regularization for the Particle Transition Amplitude in Curved Space
Abstract
We compute the perturbative short-time expansion for the transition amplitude of a particle in curved space time, by employing Dimensional Regularization (DR) to treat the divergences which occur in some Feynman diagrams. The present work generalizes known results where DR was applied to the computation of one-loop effective actions, which in the worldline approach are linked to particle path integrals on the circle, i.e. with periodic boundary conditions. The main motivation of the present work comes from revived interest in particle transition amplitudes in curved space-times, due to their use in the recently proposed worldline quantum field theory (in curved space-time).
Cite
@article{arxiv.2109.11804,
title = {Dimensional Regularization for the Particle Transition Amplitude in Curved Space},
author = {Olindo Corradini and Luigi Crispo and Maurizio Muratori},
journal= {arXiv preprint arXiv:2109.11804},
year = {2022}
}
Comments
17 pages. Discussion improved, typos corrected. Matches the published version