Explicit calculation of partition functions for a constant vacuum gauge potential

The partition function and thermodynamic potential are calculated in arbitrary space-time dimension $d$ for scalar and spinor fields coupled to a constant vacuum gauge potential $g{A}_0$ at finite temperature $T$. For $d=2, 4, 6, \dots$, closed expressions in terms of Bernoulli polynomials are obtained. This generalizes known results for $d=4\mathrm{}$.