Nonlocal quantum dynamics of the aharonov-bohm effect

The answer to the question 'when does the AB effect occur?' is elusive, for in every gauge the relative phase between the two wave packets evolves differently. Considering gauge-invariant modulo momentum, i.e., the displacement operator e^{i/h(p→ - e/c A→)L→ ·} or its Hermitian counterpart cos 1/h (p→ - e/c A→) ·L→, it is found that when the external particle's two wave packets become co-linear with the solenoid, an abrupt nonlocal exchange of the conserved quantity occurs. Using the Heisenberg picture, we show that this exchange is responsible for the shift of the interference pattern of the AB effect. We also describe a gedanken experiment that shows that our prediction can, in principle, be tested experimentally. Finally, this exchange gives new insight into the famous twoslit quantum interference experiment.