Canonical quantization of photons in a Rindler wedge

Abstract

Photons and thermal photons are studied in the Rindler wedge employing Feynman’s gauge and canonical quantization. A Gupta–Bleuler-like formalism is explicitly implemented. Nonthermal Wightman functions and related (Euclidean and Lorentzian) Green functions are explicitly calculated and their complex time analytic structure is carefully analyzed using the Fulling–Ruijsenaars master function. The invariance of the advanced minus retarded fundamental solution is checked and a Ward identity discussed. It is suggested that the KMS condition can be implemented to define thermal states also dealing with unphysical photons. Following this way, thermal Wightman functions and related (Euclidean and Lorentzian) Green functions are built up. Their analytic structure is carefully examined employing a thermal master function as in the nonthermal case and other corresponding properties are discussed. Some subtleties arising dealing with unphysical photons in the presence of the Rindler conical singularity are pointed out. In particular, a one-parameter family of thermal Wightman and Schwinger functions with the same physical content is proved to exist due to a remaining (nontrivial) static gauge ambiguity. A photon version of the Bisognano–Wichmann theorem is investigated in the case of photons propagating in the Rindler Wedge employing Wightman functions. In spite of the found ambiguity in defining Rindler Green functions, the coincidence of (β=2π)-Rindler Wightman functions and Minkowski Wightman functions is proved dealing with test functions related to physical photons and Lorentz photons.