Equivalence of the Path Integral for Fermions in Flat Spacetime in Cartesian and Spherical Coordinates

Details Equivalence of the Path Integral for Fermions in Flat Spacetime in Cartesian and Spherical Coordinates Equivalence of the Path Integral for Fermions in Flat Spacetime in Cartesian and Spherical Coordinates

2011-09-27

arxiv.org/abs/1109.5846v1

Physics

High Energy Physics

High Energy Physics - Theory

11 pages

Scientific paper

The path-integral calculation for the free energy of a fermion gas in flat spacetime is performed in spherical coordinates, and its equivalence with Cartesian coordinates is established. An appropriate generalization of spherical harmonics for fermion fields is used. The latter technique has been developed by the authors of this paper to perform the calculation of the free energy of a fermion gas in the presence of a Schwarzschild background, using a near-horizon expansion approach. The robustness of this equivalence in the flat-spacetime limit lends support to the black hole background computation leading to black hole thermodynamics.

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