  Fourier expansion of the integrand in the path integral formula for the
partition function of quantum systems leads to a deterministic expression
which, though still quite complex, is easier to process than the original
functional integral. It therefore can give access to problems that eluded
solution so far. Here we derive the formula; applications to the problem of
Bose-Einstein condensation are presented in the papers arXiv:2108.02659
[math-ph] and arXiv:2208.08931 [math-ph].
