S.P. Gavrilov, D.M. Gitman, A.A. Smirnov
Green Functions of the Dirac Equation with Magnetic-Solenoid Field
Preprint series: ESI preprints

MSC:

81Q05 Closed and approximate solutions to the Schrodinger, Dirac, Klein-Gordon and other quantum-mechanical equations

81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis

81T40 Two-dimensional field theories, conformal field theories, etc.

81V10 Electromagnetic interaction; quantum electrodynamics

PACS: 03.65.Pm,11.10.-z,11.10.Kk,12.20.-m,12.20.Ds
Abstract: Various Green functions of the Dirac equation with a magnetic-solenoid field
(the superposition of the Aharonov-Bohm field and a collinear uniform
magnetic field) are constructed and studied. The problem is considered in $%
2+1$ and $3+1$ dimensions for the natural extension of the Dirac operator
(the extension obtained from the solenoid regularization). Representations
of the Green functions as proper time integrals are derived. The
nonrelativistic limit is considered. For the sake of completeness the Green
functions of the Klein-Gordon particles are constructed as well.
Keywords: Dirac equation, Green functions, Aharonov-Bohm effect, selfadjoint extensions