Dirac fermions in a magneticsolenoid field
Abstract
We consider the Dirac equation with a magneticsolenoid field (the superposition of the AharonovBohm solenoid field and a collinear uniform magnetic field). Using von Neumann's theory of the selfadjoint extensions of symmetric operators, we construct a oneparameter family and a twoparameter family of selfadjoint Dirac Hamiltonians in the respective 2+1 and 3+1 dimensions. Each Hamiltonian is specified by certain asymptotic boundary conditions at the solenoid. We find the spectrum and eigenfunctions for all values of the extension parameters. We also consider the case of a regularized magneticsolenoid field (with a finiteradius solenoid field component) and study the dependence of the eigenfunctions on the behavior of the magnetic field inside the solenoid. The zeroradius limit yields a concrete selfadjoint Hamiltonian for the case of the magneticsolenoid field. In addition, we consider the spinless particle in the regularized magneticsolenoid field. By the example of the radial Dirac Hamiltonian with the magneticsolenoid field, we present an alternative, more simple and efficient, method for constructing selfadjoint extensions applicable to a wide class of singular differential operators.
 Publication:

arXiv eprints
 Pub Date:
 August 2003
 arXiv:
 arXiv:hepth/0308093
 Bibcode:
 2003hep.th....8093G
 Keywords:

 High Energy Physics  Theory;
 Mathematical Physics;
 Quantum Physics
 EPrint:
 33 pages, 2 figures, LaTex file