Emergent electrodynamics from the Nambu model for spontaneous Lorentz symmetry breaking

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 nonlinear gauge A μAμ=n2M2. Our result is nonperturbative in the parameter M for n2-0 and can be extended to the n2=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 nonobservable.