Mass for Plasma Photons from Gauge Symmetry Breaking

TL;DR

This paper develops a quantum field theory framework to derive effective photon masses in unmagnetized plasma, introducing a gauge symmetry breaking mechanism and a covariant approach that distinguishes longitudinal and transverse photon masses.

Contribution

It applies gauge symmetry breaking and covariant quantum field theory methods to plasma physics, providing a novel interpretation of plasma photon masses and their physical origins.

Findings

Derived effective masses for plasma photons using QFT.

Identified the physical role of the second vector field in plasma.

Provided a covariant, gauge-invariant framework for plasma photon mass analysis.

Abstract

We derive the effective masses for photons in unmagnetized plasma waves using a quantum field theory with two vector fields (gauge fields). In order to properly define the quantum field degrees of freedom we re-derive the classical wave equations on light-front gauge. This is needed because the usual scalar potential of electromagnetism is, in quantum field theory, not a physical degree of freedom that renders negative energy eigenstates. We also consider a background local fluid metric that allows for a covariant treatment of the problem. The different masses for the longitudinal (plasmon) and transverse photons are in our framework due to the local fluid metric. We apply the mechanism of mass generation by gauge symmetry breaking recently proposed by the authors by giving a non-trivial vacuum-expectation-value to the second vector field (gauge field). The Debye length $\lambda_D$ is interpreted as an effective compactification length and we compute an explicit solution for the large gauge transformations that correspond to the specific mass eigenvalues derived here. Using an usual quantum field theory canonical quantization we obtain the usual results in the literature. Although none of these ingredients are new to physicist, as far as the authors are aware it is the first time that such constructions are applied to Plasma Physics. Also we give a physical interpretation (and realization) for the second vector field in terms of the plasma background in terms of known physical phenomena. Addendum: It is given a short proof that equation (10) is wrong, therefore equations (12-17) are meaningless. The remaining results are correct being generic derivations for nonmagnetized plasmas derived in a covariant QFT framework.