  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.
