Non-perturbative approximations of path integrals with some applications to quantum statistics

Some methods for constructing uniform non-perturbative approximations of path integrals over a conditional Wiener measure are examined. The relation of these methods and the results obtained with their help to the ones known in the literature is established. The concrete analytical procedures and the formulae for the corresponding approximations are constructed and some applications in quantum statistical mechanics are considered. © 1994 Società Italiana di Fisica.