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

Fourier formula for quantum partition functions