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.

12 pages, revtex style, published version

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• Consistency of isotropic modified Maxwell theory: Microcausality and unitarity
• On the influence of a Coulomb-like potential induced by the Lorentz symmetry breaking effects on the Harmonic Oscillator
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• An investigation of the $K_F$-type Lorentz-Symmetry Breaking Gauge Models with Vortex-like Configurations
• On the superfield supersymmetric aether-like Lorentz-breaking models
• Geometric quantum phases from Lorentz symmetry breaking effects in the cosmic string spacetime
• Classical kinematics for isotropic, minimal Lorentz-violating fermion operators
• Gupta--Bleuler's quantization of the anisotropic parity-even and CPT-even electrodynamics of standard model extension