On the CPT-even Lorentz-breaking extension of the QED

In this paper, we describe the quantum electrodynamics added by Lorentz-violating CPT-even terms in the context of the standard model extension. We focus our attention on the fermion sector, represented by the CPT-even symmetric Lorentz-breaking tensor $c_{\mu\nu}$. We adopt a generic form that parametrizes the components of $c_{\mu\nu}$ in terms of one four-vector, namely, $c_{\mu\nu}=u_\mu u_\nu - \zeta \frac{u^2}{4}g_{\mu\nu}$. We then generate perturbatively, up to the third order in this tensor, the aether-like term for the gauge field. Finally, we discuss the renormalization scheme for the gauge propagator, by taking into account $c_{\mu\nu}$ traceless ($\zeta=1)$ and, trivially, $c_{\mu\nu}=u_\mu u_\nu$ ($\zeta=0$).