Emergent electrodynamics from the Nambu model for spontaneous Lorentz symmetry breaking

TL;DR

This paper demonstrates that imposing the Gauss law in the Nambu model leads to emergent QED with gauge invariance, where the photon arises as a Nambu-Goldstone mode from spontaneous Lorentz symmetry breaking.

Contribution

It shows that spontaneous Lorentz symmetry breaking in the Nambu model dynamically generates gauge invariance and reproduces QED non-perturbatively, with the photon as a Nambu-Goldstone boson.

Findings

Imposing the Gauss law yields QED in a non-linear gauge.

The result is non-perturbative in the parameter M for n^2 ≠ 0.

Electrodynamics is recovered with the photon as a Nambu-Goldstone mode.

Abstract

After imposing the Gauss law constraint as an initial condition upon the Hilbert space of the Nambu model, in all its generic realizations, we recover QED in the corresponding non-linear gauge A_{\mu}A^{\mu}=n^{2}M^{2}. Our result is non-perturbative in the parameter M for n^{2}\neq 0 and can be extended to the n^{2}=0 case. This shows that in the Nambu model, spontaneous Lorentz symmetry breaking dynamically generates gauge invariance, provided the Gauss law is imposed as an initial condition. In this way electrodynamics is recovered, with the photon being realized as the Nambu-Goldstone modes of the spontaneously broken symmetry, which finally turns out to be non-observable