Photons emerging as Goldstone bosons from spontaneous Lorentz symmetry breaking: The Abelian Nambu model

TL;DR

This paper demonstrates that photons can be viewed as Goldstone bosons resulting from spontaneous Lorentz symmetry breaking, establishing an equivalence between the Abelian Nambu model and standard QED in a specific non-linear gauge.

Contribution

It proves the equivalence of the Abelian Nambu model and QED in a non-linear gauge, showing photons as Goldstone bosons from Lorentz symmetry breaking, with all orders perturbative consistency.

Findings

The models are equivalent to all orders in perturbation theory.

Faddeev-Popov ghosts decouple in the gauge fixing process.

Photons can be interpreted as Goldstone bosons from Lorentz symmetry breaking.

Abstract

After imposing current conservation together with the Gauss law as initial conditions on the Abelian Nambu model, we prove that the resulting theory is equivalent to standard QED in the non-linear gauge $\left(A_{\mu }A^{\mu }-n^{2}M^{2}\right)=0$, to all orders in perturbation theory. We show this by writing both models in terms of the same variables, which produce identical Feynman rules for the interactions and propagators. A crucial point is to verify that the Faddeev-Popov ghosts arising from the gauge fixing procedure in the QED sector decouple to all orders. We verify this decoupling by following a method like that employed in Yang-Mills theories when investigating the behavior of axial gauges. The equivalence between the two theories supports the idea that gauge particles can be envisaged as the Goldstone bosons originating from spontaneous Lorentz symmetry breaking.