On the origin of the minimal coupling rule, and on the possiblity of   observing a classical, "Aharonov-Bohm-like" angular momentum
  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. 
Raymond Chiao
physics.class-ph quant-ph