  Yang-Mills theories supplemented by an additional coordinate constraint,
which is solved and substituted in the original Lagrangian, provide examples of
the so called Nambu models, in the case where such constraints arise from
spontaneous Lorentz symmetry breaking. Some explicit calculations have shown
that, after additional conditions are imposed, Nambu models are capable of
reproducing the original gauge theories, thus making Lorentz violation
unobservable and allowing the interpretation of the corresponding massless
gauge bosons as the Goldstone bosons arising from the spontaneous symmetry
breaking. A natural question posed by this approach in the realm of gauge
theories is to determine under which conditions the recovery of an arbitrary
gauge theory from the corresponding Nambu model, defined by a general
constraint over the coordinates, becomes possible. We refer to these theories
as extended Nambu models (ENM) and emphasize the fact that the {defining
coordinate} constraint is not treated as a standard gauge fixing term. At this
level, the mechanism for generating the constraint is irrelevant and the case
of spontaneous Lorentz symmetry breaking is taken only as a motivation, which
naturally bring this problem under consideration. Using a non-perturbative
Hamiltonian analysis we prove that the ENM yields the original gauge theory
after we demand current conservation for all time, together with the imposition
of the Gauss laws constraints as initial conditions upon the dynamics of the
ENM. The Nambu models yielding electrodynamics, Yang Mills theories and
linearized gravity are particular examples of our general approach.
