Dirac equation in the magnetic-solenoid field

Details Dirac equation in the magnetic-solenoid field Dirac equation in the magnetic-solenoid field

2002-10-31

arxiv.org/abs/hep-th/0210312v3

Eur.Phys.J.direct C30 (2003) 009; Eur.Phys.J. C32S1 (2004) 119-142

Physics

High Energy Physics

High Energy Physics - Theory

23 pages, 2 figures, LaTex file

Scientific paper

We consider the Dirac equation in the magnetic-solenoid field (the field of a solenoid and a collinear uniform magnetic field). For the case of Aharonov-Bohm solenoid, we construct self-adjoint extensions of the Dirac Hamiltonian using von Neumann's theory of deficiency indices. We find self-adjoint extensions of the Dirac Hamiltonian in both above dimensions and boundary conditions at the AB solenoid. Besides, for the first time, solutions of the Dirac equation in the magnetic-solenoid field with a finite radius solenoid were found. We study the structure of these solutions and their dependence on the behavior of the magnetic field inside the solenoid. Then we exploit the latter solutions to specify boundary conditions for the magnetic-solenoid field with Aharonov-Bohm solenoid.

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