Propagator for spinless and spin-1/2 Aharonov-Bohm-Coulomb systems

TL;DR

This paper derives the propagator for spinless and spin-1/ick Aharonov-Bohm-Coulomb systems using advanced mathematical methods, and explores their bound-state spectra, including the effects of spin and point interactions.

Contribution

It introduces a novel derivation of the propagator for these systems and connects self-adjoint extension parameters with physical coupling constants.

Findings

Derived the propagator for spinless Aharonov-Bohm-Coulomb system.

Extended the propagator to include spin-1/2 systems with point interactions.

Analyzed the bound-state energy spectra for both systems.

Abstract

The propagator of the spinless Aharonov-Bohm-Coulomb system is derived by following the Duru-Kleinert method. We use this propagator to explore the spin-1/2 Aharonov-Bohm-Coulomb system which contains a point interaction as a Zeeman term. Incorporation of the self-adjoint extension method into the Green's function formalism properly allows us to derive the finite propagator of the spin-1/2 Aharonov-Bohm-Coulomb system. As a by-product, the relation between the self-adjoint extension parameter and the bare coupling constant is obtained. Bound-state energy spectra of both spinless and spin-1/2 Aharonov-Bohm-Coulomb systems are examined.