Dimensional regularization of the path integral in curved space on an infinite time interval

Abstract

We use dimensional regularization to evaluate quantum mechanical path integrals in arbitrary curved spaces on an infinite time interval. We perform 3-loop calculations in Riemann normal coordinates, and 2-loop calculations in general coordinates. It is shown that one only needs a covariant two-loop counterterm (V_{DR} = R/8) to obtain the same results as obtained earlier in other regularization schemes. It is also shown that the mass term needed in order to avoid infrared divergences explicitly breaks general covariance in the final result.