Quantized Vector Potential and the Magnetic Aharonov-Bohm Effect

          @misc{ scivideos_PIRSA:16060055,
            doi = {10.48660/16060055},
            url = {https://pirsa.org/16060055},
            author = {Pearle, Philip},
            keywords = {Quantum Foundations},
            language = {en},
            title = {Quantized Vector Potential and the Magnetic Aharonov-Bohm Effect},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2016},
            month = {jun},
            note = {PIRSA:16060055 see, \url{https://scivideos.org/index.php/pirsa/16060055}}
          }
          

Abstract

The state vector describing the physical situation of the magnetic A-B effect should depend upon all three quantizeable entities in the problem, the electron orbiting the solenoid, the moving charged particles in the solenoid and the vector potential. One may imagine three approximate solutions to the exact dynamics, where two of the three entities do not interact at all, and the third, quantized, entity interacts with a classical approximation. Thus, fifty-five years ago, A-B showed that, if the interaction is between the quantized electron current and the classical approximation to the solenoid’s vector potential, the state vector acquires a measurable phase shift. Four years ago Vaidman showed that, if the interaction is between the quantized solenoid current and the classical approximation to the electron’s vector potential, the state vector acquires the A-B phase shift. I shall first show why these two results have to be the same. Then, I shall show that, if the interaction is between the quantized vector potential and the classical approximation to the electron and solenoid currents, the state vector acquires the A-B phase shift. Lastly, I shall show how to reconcile these three mathematically and conceptually different calculations.