Aharonov–Bohm Effect, Flat Connections, and Green's Theorem

@article{Aguilar2002AharonovBohmEF,
  title={Aharonov–Bohm Effect, Flat Connections, and Green's Theorem},
  author={M. A. Aguilar and M. Socolovsky},
  journal={International Journal of Theoretical Physics},
  year={2002},
  volume={41},
  pages={839-860}
}
The validity of Green's theorem, and hence of Stokes' theorem, when the involved vector field is differentiable but not continuously differentiable, is crucial for a theoretical explanation of the Aharonov–Bohm (A-B) effect; we review this theorem. We describe the principal bundle in which the A-B effect occurs, and give the geometrical description of the relevant connection. We study the set of gauge equivalence classes of flat connections on a product bundle with abelian structural group, and… Expand

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