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

TL;DR

This paper derives the Feynman propagator for nonbirefringent CPT-even electrodynamics within the Standard Model Extension, analyzing stability, causality, and unitarity, and clarifying properties of parity sectors.

Contribution

It provides an explicit calculation of the gauge propagator for nonbirefringent CPT-even components, including new insights into stability and causality of the theory.

Findings

The propagator is explicitly evaluated in a tensor form.

The parity-even sector is shown to be stable, noncausal, and unitary.

The results clarify and extend previous literature on the topic.

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.