Semiclassical approximation to the partition function of a particle in D dimensions

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