Quantized vector potential and alternative views of the magnetic Aharonov-Bohm phase shift

@article{Pearle2017QuantizedVP,
  title={Quantized vector potential and alternative views of the magnetic Aharonov-Bohm phase shift},
  author={Philip Mark Pearle and Anthony Rizzi},
  journal={Physical Review A},
  year={2017},
  volume={95},
  pages={052124}
}
We give a complete quantum analysis of the Aharonov-Bohm (AB) magnetic phase shift involving three entities: the electron, the charges constituting the solenoid current, and the vector potential. The usual calculation supposes that the solenoid's vector potential may be well approximated as classical. The AB shift is then acquired by the quantized electron moving in this vector potential. Recently, Vaidman presented a semiclassical calculation [L. Vaidman, Phys. Rev. A 86, 040101 (2012)], later… 
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