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

Abstract

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, $c_{\mu \nu }=u_{\mu }{u}_{\nu }$ ($\zeta =0$).

19 pages, Preprint of an article submitted for consideration in Int. J. Mod. Phys. A \c{opyright} 2017 [copyright World Scientific Publishing Company] [http://www.worldscientific.com/worldscinet/ijmpa]

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