  In this dissertation, we study the implications generated by the Lorentz
breaking symmetry in quantum electrodynamics. We analyze fermions interacting
with an electromagnetic field in the contexts of quantum mechanics and make
radiative corrections. In quantum mechanics, the terms of the Lorentz breaking
symmetry were treated as perturbations to the Dirac equation, and their
expected values were obtained in a vacuum. In the radiative corrections, the
Lorentz breaking symmetry was introduced in this interaction for the
Chern-Simons like term could be induced in (3 +1) dimensions. We also discussed
the consequences generated by this term on the propagation speeds of classic
photons.
