Stationary solutions for the parity-even sector of the CPT-even and Lorentz-covariance-violating term of the standard model extension

TL;DR

This paper investigates how parity-even Lorentz-violating terms in the CPT-even sector of the standard model extension affect classical electromagnetic solutions, providing explicit solutions and potential experimental bounds.

Contribution

It offers explicit stationary solutions for modified Maxwell equations with Lorentz-violating parameters and proposes an Earth-based experiment to bound these coefficients.

Findings

Parity-even terms do not couple electric and magnetic fields in stationary regime.

Explicit solutions for E and B fields for point-like and extended sources.

Potential to set upper bounds on Lorentz-violating coefficients as low as 2.9×10^{-20}.

Abstract

In this work, we focus on some properties of the parity-even sector of the CPT-even electrodynamics of the standard model extension. We analyze how the six non-birefringent terms belonging to this sector modify the static and stationary classical solutions of the usual Maxwell theory. We observe that the parity-even terms do not couple the electric and magnetic sectors (at least in the stationary regime). The Green's method is used to obtain solutions for the field strengths E and B at first order in the Lorentz- covariance-violating parameters. Explicit solutions are attained for point-like and spatially extended sources, for which a dipolar expansion is achieved. Finally, it is presented an Earth-based experiment that can lead (in principle) to an upper bound on the anisotropic coefficients as stringent as $(\widetilde{\kappa}_{e-}) ^{ij}<2.9\times10^{-20}.$