Equivalence of the Path Integral for Fermions in Cartesian and Spherical   Coordinates
  The path-integral calculation for the free energy of a spin-1/2 Dirac-fermion gas is performed in spherical polar coordinates for a flat spacetime geometry. Its equivalence with the Cartesian-coordinate representation is explicitly established. This evaluation involves a relevant limiting case of the fermionic path integral in a Schwarzschild background, whose near-horizon limit has been shown to be related to black hole thermodynamics. 
Andrew Briggs, Horacio E. Camblong, Carlos R. Ordonez
hep-th math-ph math.MP