On the origin of the minimal coupling rule, and on the possiblity of observing a classical, "Aharonov-Bohm-like" angular momentum

TL;DR

This paper derives the classical minimal coupling rule from relativistic action principles and proposes macroscopic experiments to observe electromagnetic angular momentum analogous to the Aharonov-Bohm effect.

Contribution

It provides a classical derivation of the minimal coupling rule and suggests experiments to observe Aharonov-Bohm-like phenomena at a macroscopic level.

Findings

Derivation of minimal coupling from classical action

Proposal of experiments to observe classical electromagnetic angular momentum

Connection between classical and quantum Aharonov-Bohm effects

Abstract

The minimal coupling rule is "derived" starting from Landau's relativistically invariant classical action for a charge in the presence of classical electromagnetic fields. Experiments are then proposed to see the resulting electromagnetic angular momentum of a classical, "lumpy" charged ring enclosing a solenoid. These classical, macroscopic experiments are similar in spirit to those proposed by Aharonov and Bohm at the quantum level.