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Stokes' theorem, gauge symmetry and the time-dependent Aharonov-Bohm effect

### Abstract

Stokes' theorem is investigated in the context of the time-dependent Aharonov-Bohm effect—the two-slit quantum interference experiment with a time varying solenoid between the slits. The time varying solenoid produces an electric field which leads to an additional phase shift which is found to exactly cancel the time-dependent part of the usual magnetic Aharonov-Bohm phase shift. This electric field arises from a combination of a non-single valued scalar potential and/or a 3-vector potential. The gauge transformation which leads to the scalar and 3-vector potentials for the electric field is non-single valued. This feature is connected with the non-simply connected topology of the Aharonov-Bohm set-up. The non-single valued nature of the gauge transformation function has interesting consequences for the 4-dimensional Stokes' theorem for the time-dependent Aharonov-Bohm effect. An experimental test of these conclusions is proposed.

© 2014 AIP Publishing LLC

Received 13 December 2013
Accepted 11 March 2014
Published online 01 April 2014

Acknowledgments:
D.S. thanks Sodsri Singleton for her support during the period when this work was completed. J.M. acknowledges the support of Donna Ramacciotti.

Article outline:

I. INTRODUCTION
II. STOKES' THEOREM USING DIFFERENTIAL FORMS
III. TIME-DEPENDENT AHARONOV-BOHM EFFECT
IV. SINUSOIDAL FLUX VARIATION
V. MULTIVALUED MONOPOLE POTENTIAL
VI. SUMMARY

/content/aip/journal/jmp/55/4/10.1063/1.4869324

http://aip.metastore.ingenta.com/content/aip/journal/jmp/55/4/10.1063/1.4869324

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