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

We use dimensional regularization to evaluate quantum mechanical path integ rals 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 = (h2)/R-8) to obtain the same results as obtained earlie r in other regularization schemes. It is also shown that the mass term need ed in order to avoid infrared divergences explicitly breaks general covaria nce in the final result. (C) 2000 Elsevier Science B.V. All rights reserved .