Canonical Quantization of Photons in a Rindler Wedge

TL;DR

This paper develops a canonical quantization framework for photons in a Rindler wedge, analyzing thermal and non-thermal states, Green functions, and gauge ambiguities, extending quantum field theory in curved spacetime.

Contribution

It introduces a Gupta-Bleuler-like formalism for photons in Rindler space, explicitly calculates Green functions, and explores gauge ambiguities and the Bisognano-Wichmann theorem in this context.

Findings

Explicit calculation of Wightman and Green functions in Rindler space.

Identification of gauge ambiguities affecting thermal Green functions.

Proof of the coincidence of Rindler and Minkowski Wightman functions for physical photons.

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. Non thermal Wightman functions and related (Euclidean and Lorentzian) Green functions are explicitly calculated and their complex time analytic structure is 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 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 examined employing a thermal master function as in the non thermal case and other corresponding properties are discussed. Some subtleties arising dealing with unphysical photons in presence of the Rindler conical singularity are pointed out. In particular, a family of thermal Wightman and Schwinger functions with the same physical content is proved to exist due to a remaining static gauge ambiguity. A photon version of Bisognano-Wichmann theorem is investigated in the case of photons propagating in the Rindler Wedge employing Wightman functions. Despite of the found ambiguity in defining Rindler Green functions, the coincidence of $(\beta = 2\pi)$-Rindler Wightman functions and Minkowski Wightman functions is proved dealing with test functions related to physical photons and Lorentz photons.