Scattering wave functions for Aharonov-Bohm-Coulomb field: Path integral treatment

TL;DR

This paper analytically derives Green's functions and scattering wavefunctions for a Dirac particle in combined Aharonov-Bohm and Coulomb fields using path integral formalism, revealing properties of the spinors and their energy spectra.

Contribution

It provides an exact path integral-based calculation of Green's functions and scattering states for Dirac particles in Aharonov-Bohm-Coulomb fields, facilitating analysis of their properties.

Findings

Exact Green's functions for the combined fields are obtained.

Scattering wavefunctions and energy eigenvalues are explicitly derived.

Properties of spinors under the combined fields are analyzed.

Abstract

Exact Green's functions related to Dirac particle submitted to the combination of Aharonov-Bohm and Coulomb fields in (2+1) coordinate space are analytically calculated via path integral formalism in both global and local representations. The scattering normalized wavefunctions as well as the corresponding continuous energy eigenvalues are extracted following this approach. The interesting properties of the spinors are thus deduced after symmetrization. According to the symmetric form for the Green's function, it is shown that the equivalence with Dirac equation is undertaken with much ease. Some particular cases are also considered.