In this dissertation we study dynamic Lorentz symmetry breaking, that is, the spontaneous symmetry breaking induced by radiative corrections of a self-interacting fermionic theory. In our study we verified that after introducing an antisymmetric tensor auxiliary field, we obtain a theory with this field minimally coupled to a spinor, in which we calculate the effective potential of a loop, at zero temperature and finite temperature, and also the effective action of a loop. After computing the zero-temperature gap equation of the effective potential, we explicitly demonstrate that the resulting potential is positively defined and has a continuous set of minima. We also investigate the conditions for symmetry restoration when we calculate the gap equation at finite temperature, in which we obtain certain constraints on the antisymmetric components of the tensor field. Furthermore, we get the same second-order kinetic action on fields when we consider the effective action of a loop with the left-right derivative or just one derivative.