Explicit evaluation of certain Gaussian functional integrals arising in problems of statistical physics

Abstract
An explicit formula is presented for a (conditional) Wiener integral, the integrand of which is an exponential of a general quadratic functional of the path. The functional integrals arising in non-Markovian Gaussian approximations to various problems of statistical physics (e.g., theory of the large polaron, theory of disordered systems) are easily recovered as special cases.