Green functions of the Dirac equation with magnetic-solenoid field

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.

arXiv comment12 pages, LaTex file; added references and some comments; accepted to J.Math.Phys

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Cited by in corpus (5)

• Zero modes in a system of Aharonov-Bohm fluxes
• On Painleve VI transcendents related to the Dirac operator on the hyperbolic disk
• Symmetry operators and separation of variables in the $(2+1)$-dimensional Dirac equation with external electromagnetic field
• Induced Current and Aharonov-Bohm Effect in Graphene
• Position-space representation of charged particles' propagators in a constant magnetic field as an expansion over Landau levels