The Aharonov–Bohm problem revisited

Abstract

The properties of a nonrelativistic charged particle in two-dimensions in the presence of an arbitrary number of nonquantized magnetic fluxes are investigated in free space as well as in a uniform magnetic field. The fluxes are represented mathematically as branch points in one of the complex@ coordinates. To construct many-flux solutions without a magnetic field, however, the fluxes must be treated as dynamical objects dual to the charges. A medium made up of fluxes acts like an anti-magnetic field and tends to expel the charges.

Solutions of relativistic wave equations in superpositions of Aharonov–Bohm, magnetic, and electric fields

“…AB scattering for spinning particles was considered in [4] and [5] using exact solutions of Dirac equation in the AB field. A number of theoretical works and convinced experiments were done to clarify AB effect and to prove its existence (see, for example, [6][7][8][9]). …”

Multidimensional Dirac strings and the Witten index of SYMCS theories with groups of higher rank

“…Thus, to get a nice normalizable zero mode, we need to compactify the complex plane. It is usually done by replacing C → S 2 [20,21] , but compactification on the torus is also possible [22].…”

Zero Modes in a System of Aharonov–bohm Fluxes

“…The multi-solenoid case is more difficult because of the rotational symmetry violation. This case was treated by means of the Krein resolvent formula in [44], and for an infinite chain of solenoids in [45]; different approaches are presented in [46,47,48]. The problem of defining the boundary conditions at the presence of a uniform background field has been investigated in [49,50].…”