Maximally symmetric nonlinear extension of electrodynamics and charged particles

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.