There is a symmetry in physics which we might call the Local Phase Symmetry in quantum mechanics. In this symmetry we change the phase of the (electron) wavefunction by a different amount everywhere in spacetime. To compensate for this change, we need to also make a gauge transformation of the electromagnetic potentials. They all must go together like this.
We exploit the gauge symmetry in EM to show that, in field free regions,
can be simply equal to a line integral of the vector potential
(if we pick the right gauge).
We also show that magnetic fields can be used to change interference effects in quantum mechanics. The Aharanov Böhm Effect brings us back to the two slit diffraction experiment but adds magnetic fields.
Jim Branson 2013-04-22