Optical Approach for the Thermal Partition Function of Photons

The optical manifold method to compute the one-loop effective action in a static space-time is extended from the massless scalar field to the Maxwell field in any Feynman-like covariant gauge. The method is applied to the case of the Rindler space obtaining the same results as the point-splitting procedure. The result is free from Kabat's surface terms which instead affect the $\zeta$-function or heat-kernel approaches working directly in the static manifold containing conical singularities. The relation between the optical method and the direct $\zeta$-function approach on the Euclidean Rindler manifold is discussed both in the scalar and the photon cases. Problems with the thermodynamic self-consistency of the results obtained from the stress tensor in the case of the Rindler space are pointed out.