In one minute

Pablo Saldanha demonstrates that the Aharonov-Bohm effect is gauge invariant when the electromagnetic field is treated quantum mechanically. He solves exactly, in the Lorenz gauge, for the ground energy of the quantum field interacting with the classical charges and currents that source the potentials. First-order perturbation theory then gives the extra energy from a charged quantum particle, which depends on its path through an interferometer and so produces the Aharonov-Bohm phase difference. The phase difference is shown to be gauge invariant for the magnetic, electric and recently proposed electrodynamic versions of the effect. For open paths the phase could depend on the gauge, reinforcing that it is measurable only around closed paths.

Gauge invariance of the Aharonov-Bohm effect in a quantum electrodynamics framework