On one-loop corrections to the CPT-even Lorentz-breaking extension of 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 [Formula: see text]. We adopt a generic form that parametrizes the components of [Formula: see text] in terms of one four-vector, namely, [Formula: see text]. 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 [Formula: see text] traceless [Formula: see text] and, trivially, [Formula: see text] [Formula: see text].