  The quantization of a vector model presenting spontaneous breaking of Lorentz
symmetry in flat Minkowski spacetime is discussed. The Stueckelberg trick of
introducing an auxiliary field along with a local symmetry in the initial
Lagrangian is used to convert the second-class constraints present in the
initial Lagrangian to first-class ones. An additional deformation is employed
in the resulting Lagrangian to handle properly the first-class constraints, and
the equivalence with the initial model is demonstrated using the BRST
invariance of the deformed Lagrangian. The framework for performing
perturbation theory is constructed and the structure of the Fock space is
discussed. Despite the presence of ghost and tachyon modes in the spectrum of
the theory, it is shown that one can implement consistent conditions to define
a unitary and stable reduced Fock space. Within the restricted Fock space, the
free model turns out to be equivalent to the Maxwell electrodynamics in the
temporal gauge.
