Symmetry theory of the Aharonov-Bohm effect: Quantum mechanics in a multiply connected region

Lindsay J Tassie, Murray Peshkin

Yakir Aharonov, C. K. Au, E. C. Lerner +1 more

G. Morandi, E Menossi

The motion of a nonrelativistic charged particle in a plane, multiply-connected region is studied within the framework of Feynman's path-integral approach to quantum mechanics. In particular, the authors study the simple case when the multiply-connected region is obtained by excluding a disc from the plane. If a nonzero magnetic flux is confined inside the disc, this is shown to include a change in the one-dimensional unitary representation of the fundamental group of the space which enters a proper definition of the path-integral. In this way, a simple explanation of the Aharonov-Bohm effect is shown to arise.

Chris Philippidis, David Böhm, R.D. Kaye

W P Healy, Ranjith Ananda Samandra

The electric Aharonov-Bohm effect is usually explained by means of the scalar potential, which is present in a multiply connected region of space time where no electric field acts on the charged particle. An alternative interpretation is given in terms of the particle's polarization field penetrating the region occupied by the electric field but inaccessible to the particle itself. Similarly, the magnetic Aharonov-Bohm effect is usually explained by means of the vector potential, which is present in a multiply connected region of space where no magnetic-induction field acts on the charged particle. An alternative interpretation of this effect is given in terms of the particle's magnetization field penetrating the region occupied by the magnetic-induction field but inaccessible to the particle itself. Our interpretations of the electric and magnetic Aharonov-Bohm effects are both developed by using the multipolar form of the Lagrangian instead of the minimal-coupling form in the Feynman path integral.

A.I. Vainshtein, В. В. Соколов