Topology, nonlocality and duality in classical electrodynamics

TL;DR

This paper explores topological and nonlocal electromagnetic angular momentum in classical electrodynamics, demonstrating a duality-invariant quantity that depends on winding numbers and is unaffected by radiative effects.

Contribution

It introduces a duality-invariant electromagnetic angular momentum unifying topological and nonlocal effects in classical electrodynamics.

Findings

The angular momentum depends on a winding number, indicating its topological nature.

It remains invariant under electromagnetic duality transformations.

The angular momentum is insensitive to radiative effects of Lie9nard-Wiechert fields.

Abstract

We have recently (Heras et al. in Eur. Phys. J. Plus 136:847, 2021) argued that classical electrodynamics can predict nonlocal effects by showing an example of a topological and nonlocal electromagnetic angular momentum. In this paper we discuss the dual of this angular momentum which is also topological and nonlocal. We then unify both angular momenta by means of the electromagnetic angular momentum arising in the configuration formed by a dyon encircling an infinitely-long dual solenoid enclosing uniform electric and magnetic fluxes and show that this electromagnetic angular momentum is topological because it depends on a winding number, is nonlocal because the electric and magnetic fields of this dual solenoid act on the dyon in regions for which these fields are excluded and is invariant under electromagnetic duality transformations. We explicitly verify that this duality-invariant electromagnetic angular momentum is insensitive to the radiative effects of the Li\'enard-Wiechert fields of the encircling dyon. We also show how duality symmetry of this angular momentum suggests different physical interpretations for the corresponding angular momenta that it unifies.