Regular Article - Theoretical Physics
Dimensional regularization for the particle transition amplitude in curved space
Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Università degli Studi di Modena e Reggio Emilia, Via Campi 213/A, 41125, Modena, Italy
2 INFN, Sezione di Bologna, Via Irnerio 46, 40126, Bologna, Italy
Accepted: 13 January 2022
Published online: 25 January 2022
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).
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