Dimensional Regularization for the Particle Transition Amplitude in Curved Space

TL;DR

This paper applies Dimensional Regularization to compute the short-time expansion of a particle's transition amplitude in curved spacetime, advancing the understanding of quantum effects in curved backgrounds.

Contribution

It generalizes the use of Dimensional Regularization to particle transition amplitudes in curved space, extending previous one-loop effective action computations to more complex scenarios.

Findings

Successfully computed perturbative short-time expansion using DR

Extended DR techniques to curved spacetime particle amplitudes

Enhanced understanding of quantum effects in curved backgrounds

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).