  We use a path integral formalism to derive the semiclassical series for the
partition function of a particle in D dimensions. We analyze in particular the
case of attractive central potentials, obtaining explicit expressions for the
fluctuation determinant and for the semiclassical two-point function in the
special cases of the harmonic and single-well quartic anharmonic oscillators.
The specific heat of the latter is compared to precise WKB estimates. We
conclude by discussing the possible extension of our results to field theories.
