Dispersion Relations in Non-Linear Electrodynamics and the Kinematics of the Compton Effect in a Magnetic Background

TL;DR

This paper investigates how non-linear electrodynamics affects the kinematics of the Compton effect in magnetic backgrounds, deriving dispersion relations and constraints for various models to understand photon behavior in external fields.

Contribution

It provides a general framework for non-linear electrodynamics in magnetic backgrounds and analyzes the Compton effect kinematics within specific models, deriving new constraints.

Findings

Derived dispersion relations and refraction indices in external magnetic fields.

Established constraints relating Lagrangian derivatives to magnetic backgrounds.

Analyzed specific models like Euler-Heisenberg and Born-Infeld for their effects on photon kinematics.

Abstract

Non-linear electrodynamic models are re-assessed in this paper to pursue an investigation of the kinematics of the Compton effect in a magnetic background. Before considering specific models, we start off by presenting a general non-linear Lagrangian built up in terms of the most general Lorentz- and gauge-invariant combinations of the electric and magnetic fields. The extended Maxwell-like equations and the energy-momentum tensor conservation are presented and discussed in their generality. We next expand the fields around a uniform and time-independent electric and magnetic backgrounds up to second order in the propagating wave, and compute dispersion relations which account for the effect of the external fields. We obtain thereby the refraction index and the group velocity for the propagating radiation in different situations. In particular, we focus on the kinematics of the Compton effect in presence of external magnetic fields. This yields constraints that relate the derivatives of the general Lagrangian with respect to the field invariants and the magnetic background under consideration. We carry out our inspection by focusing on some specific non-linear electrodynamic effective models: Hoffmann-Infeld, Euler-Heisenberg, generalized Born-Infeld and Logarithmic.