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

C. A. A. de Carvalho, R. M. Cavalcanti, E. S. Fraga, S. E. Jorás

Published 1999-10-13, updated 2000-03-15Version 2

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.