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 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(u2)(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).