Green functions of the Dirac equation with magnetic-solenoid field

Details Green functions of the Dirac equation with magnetic-solenoid field Green functions of the Dirac equation with magnetic-solenoid field

2003-10-07

arxiv.org/abs/math-ph/0310007v2

J.Math.Phys. 45 (2004) 1873-1886

Physics

Mathematical Physics

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

Scientific paper

10.1063/1.1699483

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.

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