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Proof of summed form of proper-time expansion for propagator in curved space-time.

We consider the Schwinger-DeWitt proper-time expansion of the kernel of the Feynman propagator in curved space-time. We prove that the proper-time expansion can be written in a new form, conjectured by Parker and Toms, in which all the terms containing the scalar curvature R are generated by a simple overall exponential factor. This sums all terms containing R, including those with nonconstant coefficients, in the proper-time series. This result is valid for an arbitrary space-time and for any spin. It also applies to the heat kernel. This form of the expansion is of importance in connection with nonperturbative effects in quantum field theory.