  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).
