  In this paper, the induced Chern-Simons like action for a system of fermions
interacting with a gauge field in (3 +1) dimensions is calculated in the
presence of a background field that breaks the Lorentz and CPT symmetries. The
main result of this work corresponds to the obtation of a usual
Chern-Simons-type action in four-dimensional spacetime resulting from the
addition to the conventional QED Lagrangian of a term with a background field
that breaks the Lorentz symmetry of the Lagrangian gauge theory. It is pointed
out that the proportionality constant in that term depends heavily on the
regularization method used in the computations. As the articles on this subject
in the literature are very difficult to read, here calculations are performed
clearly and objectively.

High Energy Physics - Theory