Massless and Massive Vector Goldstone Bosons in Nonlinear Quantum Electrodynamics

TL;DR

This paper investigates spontaneous Lorentz invariance violation in nonlinear QED with a vector field constraint, revealing the emergence of vector Goldstone bosons that are massless or massive depending on symmetry breaking, yet observable Lorentz invariance remains intact.

Contribution

It demonstrates how SLIV in nonlinear QED leads to vector Goldstone bosons and shows that physical Lorentz invariance is preserved despite apparent violations.

Findings

Vector Goldstone bosons emerge from SLIV in nonlinear QED.

Massless or massive vector bosons depend on U(1) symmetry breaking.

Observable processes do not exhibit Lorentz violation.

Abstract

The spontaneous Lorentz invariance violation (SLIV) developing in QED type theories with the nonlinear four-vector field constraint $A_{\mu}^{2}=M^{2}$ (where $M$ is a proposed scale of the Lorentz violation) is considered in the case when the internal U(1) charge symmetry is also spontaneously broken. We show that such a SLIV pattern induces the genuine vector Goldstone boson which appears massless when the U(1) symmetry is exact and becomes massive in its broken phase. However, for both of phases an apparent Lorentz violation is completely canceled out in all the observable processes so that the physical Lorentz invariance in theory is ultimately restored.