Photon as a Vector Goldstone Boson: Nonlinear $\sigma $ Model for QED

TL;DR

This paper proposes that QED can be viewed as an effective low-energy theory emerging from a nonlinear sigma model where the photon acts as a vector Goldstone boson resulting from spontaneous Lorentz symmetry breaking at a high scale.

Contribution

It introduces a nonlinear sigma model framework for QED, interpreting the photon as a Goldstone boson from Lorentz symmetry breaking, connecting it to a high-energy symmetry-breaking scale.

Findings

QED in Coulomb gauge is a low-energy limit of the nonlinear sigma model.

Photon emerges as a vector Goldstone boson due to Lorentz symmetry breaking.

Model predicts Lorentz and CPT symmetry breaking terms suppressed by the high scale M.

Abstract

We show that QED in the Coulomb gauge can be considered as a low energy linear approximation of a non-linear $\sigma $-type model where the photon emerges as a vector Goldstone boson related to the spontaneous breakdown of Lorentz symmetry down to its spatial rotation subgroup at some high scale $M$. Starting with a general massive vector field theory one naturally arrives at this model if the pure spin-1 value for the vector field $A_{\mu}(x)$ provided by the Lorentz condition $\partial_{\mu}A_{\mu}(x)=0$ is required. The model coincides with conventional QED in the Coulomb gauge in the limit of M going to infinity and generates a very particular form for the Lorentz and CPT symmetry breaking terms, which are suppressed by powers of $M$.