Green functions of the Dirac equation with magnetic-solenoid field

TL;DR

This paper constructs and analyzes Green functions for the Dirac equation in a magnetic-solenoid field, extending the understanding of quantum behavior in combined magnetic and Aharonov-Bohm fields across different dimensions.

Contribution

It provides explicit Green function representations for the Dirac equation with a magnetic-solenoid field in 2+1 and 3+1 dimensions, including proper time integrals and nonrelativistic limits.

Findings

Green functions derived as proper time integrals

Nonrelativistic limit analyzed

Green functions for Klein-Gordon particles also constructed

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.