00-334 Masao Hirokawa, Osamu Ogurisu

Ground state of a spin-1/2 charged particle in a two-dimensional magnetic field (33K, REVTeX v3.1) Sep 3, 00

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Abstract. It is investigated that the structure of the kernel of the Dirac-Weyl operator \(\D\) of a charged particle in the magnetic field \(B=B_0+b\), given by the sum of a strongly singular magnetic field \(B_0(\cdot)=\sum_j\gamma^j\delta(\cdot-a_j)\) and a magnetic field \(b\) with a bounded support. Here the magnetic field \(b\) 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, {\bf{19}}, 1979], the dimension of the kernel of \(\D\), \(\dim\ker\D\), is a function of one variable, the total magnetic flux of \(B\) (\(=\int_{\R^2}b\,dx\,dy+\sum_j\gamma_j\)). % However, since the influence of the strongly singular points occurs, \(\dim\ker\D\) indeed is a function of several variables, the total magnetic flux and each of \(\gamma_j\)'s.

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