Investigações sobre a ação de Euler-Heisenberg com violação de simetria CPT

Abstract

In this work, we consider radiative corrections of an extended QED loop, with violation of Lorentz and CPT, to discuss the specific problem of finding an amplitude due to the effect of the triple division of the photon. For this, we work with a lagrangian that includes the coeffcient bµ which is a four-vector constant that regulates the Lorentz and CPT violation in the fermionic sector, whose presence affects the effect of the photon division. We performed a study on the Lorentz transformations of particle and observer, in which it was observed that in the presence of an electric field, the rotations and textit boost break the correspondence between such transformations, and we still discourse about the violation of Lorentz invariance taking into account the Extended Standard Model. The effective action was found through the Heisenberg-Euler Action, which describes the nonlinear dynamics of electromagnetic fields in vacuum, where from this action it was possible to write a mathematical expression for the analyzed diagram of four legs of photons, so that it contains the breaking of symmetry and would be viable to calculate the amplitude of the effect generated by the triple division of the photon in question. We show that there is no nonzero amplitude for the division of photons, for the non-collinear case; following the prescription of references consulted we obtained a result different from zero, in the collinear limit.