Ground state of a spin-1/2 charged particle in a two-dimensional magnetic field

Abstract

It is investigated that the structure of the kernel of the Dirac–Weyl operator D of a charged particle in the magnetic-field B=B0+B1, given by the sum of a strongly singular magnetic field B0(⋅)=Σνγνδ(⋅−aν) with some singular points aν and a magnetic-field B1 with a bounded support. Here the magnetic field B1 may have some singular points with the order of the singularity less than 2. At a glance, it seems that, following “Aharonov–Casher Theorem” [Phys. Rev. A 19, 2461 (1979)], the dimension of the kernel of D, dim ker D, is a function of one variable of the total magnetic flux (=Σνγν+∫R2B1dxdy) of B. However, since the influence of the strongly singular points works, dim ker D indeed is a function of several variables of the total magnetic flux and each of γν’s.