  In this paper, we analysis the dynamics, at the quantum level, of the
self-dual field minimally coupled to bosons with Lorentz symmetry breaking. We
quantize the model by applying the Dirac bracket canonical quantization
procedure. In addition, we test the relativistic invariance of the model by
computing the boson-boson elastic scattering amplitude. Therefore, we show that
the Lorentz symmetry breaking has been restored at the quantum level. We
finalize our analysis by computing the dual equivalence between the self-dual
model with Lorentz symmetry breaking coupled with bosonic matter and the
Maxwell-Chern-Simons with Lorentz invariance violation coupled with bosonic
field.
