Feynman propagator for the nonbirefringent CPT-even electrodynamics of the Standard Model Extension

Abstract: The CPT-even gauge sector of the Standard Model Extension is composed of nineteen components comprised in the tensor $(K_{F}){\mu \nu\rho\sigma}$, of \ which nine do not yield birefringence. In this work, we examine the Maxwell electrodynamics supplemented by these nine nonbirefringent CPT-even components in aspects related to the Feynman propagator and full consistency (stability, causality, unitarity). We adopt a prescription that parametrizes the nonbirefringent components in terms of a symmetric and traceless tensor, $K{\mu\nu},$ and second parametrization that writes $K_{\mu\nu}$ in terms of two arbitrary four-vectors, $U_{\mu}$ and $V_{\nu}.$ We then explicitly evaluate the gauge propagator of this electrodynamics in a tensor closed way. In the sequel, we show that this propagator and involved dispersion relations can be specialized for the parity-odd\ and parity-even sectors of the tensor $(K_{F})_{\mu\nu\rho\sigma}$. In this way, we reassess some results of the literature and derive some new outcomes showing that the parity-even anisotropic sector engenders a stable, noncausal and unitary electrodynamics.