Aspectos quânticos da eletrodinâmica quântica com operadores de dimensão d = 5

Abstract

The study of Lorentz symmetry violation in field theory has gained a lot of attention in recent years, mainly from the discovery that in string theory we have the possibility of spontaneous breaking of Lorentz symmetry when we take the low energy limit. These studies motivated the construction of the standard model extension (SME), which is, in fact, an extension of the usual standard model (SM), in which all possible terms that violate the Lorentz and CPT symmetries are added, respecting the gauge. The minimal SME contains only renormalizable terms, while the non-minimal SME includes all nonrenormalizable terms. In the first part of this work, we studied the non-minimal extension of Quantum Electrodynamics (QED), considering all Lorentz violation operators (LV) of mass dimension d = 5, and investigated the possibility of generating the Carroll-Field-Jackiw (CFJ) and its higher derivative counterpart on the non-minimal coupling constants. We explicitly demonstrate that there is no generation of the CFJ term when we adopt the dimensional regularization scheme. Furthermore, we show that the divergent parts of the higher derivative terms can be eliminated by considering certain proportionality relationships between the coefficients. In the second part, we consider the Horava-Lifshitz (HL) like QED with z = 3, in which we include the axial vector b0,i that breaks the CPT symmetry. For this model, we calculated the CFJ term in different regularization schemes and found that the CFJ term is finite, however, ambiguous, since it depends on the regularization scheme used. Finally, we calculate the CFJ term of this model using the functional integral approach, in which we find once again that the CFJ term is finite, but undetermined.