Geometry of the Aharonov–Bohm Effect

  title={Geometry of the Aharonov–Bohm Effect},
  author={R. S. Huerfano and M. A. L{\'o}pez and M. Socolovsky},
  journal={International Journal of Theoretical Physics},
Abstract We show that the connection responsible for any Abelian or non-Abelian Aharonov–Bohm effect with n parallel “magnetic” flux lines in ℝ3, lies in a trivial G-principal bundle P→M, i.e. P is isomorphic to the product M×G, where G is any path connected topological group; in particular a connected Lie group. We also show that two other bundles are involved: the universal covering space $\tilde{M}\to M$ , where path integrals are computed, and the associated bundle P×Gℂm→M, where the wave… Expand
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