Classical solutions for the Lorentz-violating and CPT-even term of the Standard Model Extension

TL;DR

This paper derives classical electromagnetic solutions within the Standard Model Extension considering Lorentz-violating, CPT-even terms, and establishes a new stringent bound on the LV parameter based on macroscopic magnetic field measurements.

Contribution

It provides explicit classical solutions for electrodynamics with Lorentz-violating CPT-even terms and derives a new upper bound on the LV parameter from macroscopic magnetic field data.

Findings

Charge and current produce first-order effects on electric and magnetic fields.

A dipolar expansion of the field strengths is obtained.

A bound of $^{-16}$ on the LV parameter is established.

Abstract

In this work, we calculate the classical solutions for the electrodynamics stemming from the Lorentz-violating (LV) and CPT-even term of the Standard Model Extension. The solutions for point-like and extended charges are obtained from the wave equations by means of the Green method. A dipolar expansion is written for the field strengths. It is explicitly shown that charge and current generate first order effects for the magnetic and electric fields, respectively. Using the magnetic field generated by a macroscopic 1C charged sphere, we establish a stringent bound for the LV parameter:$\kappa \leq 10^{-16}.$