Maximally symmetric nonlinear extension of electrodynamics and charged particles

TL;DR

This paper explores the unique physical effects of the ModMax non-linear electrodynamics, showing that certain classical solutions like Lienard-Wiechert fields remain exact, and examines how non-linearity influences electromagnetic interactions and quantization.

Contribution

It demonstrates that Lienard-Wiechert fields are exact solutions in ModMax, unlike in other non-linear models, and investigates the impact of ModMax on fundamental electromagnetic phenomena.

Findings

Lienard-Wiechert fields are exact solutions in ModMax

ModMax affects the properties of electromagnetic interactions

An alternative ModMax Lagrangian involving scalar fields is proposed

Abstract

We consider couplings of electrically and magnetically charged sources to the maximally symmetric non-linear extension of Maxwell's theory called ModMax. The aim is to reveal physical effects which distinguish ModMax from Maxwell's electrodynamics. We find that, in contrast to generic models of non-linear electrodynamics, Lienard-Wiechert fields induced by a moving electric or magnetic particle, or a dyon are exact solutions of the ModMax equations of motion. We then study whether and how ModMax non-linearity affects properties of electromagnetic interactions of charged objects, in particular the Lorentz force, the Coulomb law, the Lienard-Wiechert fields, Dirac's and Schwinger's quantization of electric and magnetic charges, and the Compton Effect. In passing we also present an alternative form of the ModMax Lagrangian in terms of the coupling of Maxwell's theory to axion-dilaton-like auxiliary scalar fields which may be relevant for revealing the effective field theory origin of ModMax.