Schwinger's formula and the partition function for the bosonic and   fermionic harmonic oscillator
  We use Schwinger's formula, introduced by himself in the early fifties to compute effective actions for QED, and recently applied to the Casimir effect, to obtain the partition functions for both the bosonic and fermionic harmonic oscillator. 
L.C. Albuquerque, C. Farina and S.J. Rabello