Magnetic Moment and Perturbation Theory with Singular Magnetic Fields

TL;DR

This paper investigates the spectral behavior of charged particles in singular magnetic fields, revealing how a magnetic moment interaction and wave function redefinition can resolve perturbation theory singularities.

Contribution

It introduces a novel interpretation of the contact term as a magnetic moment coupling and extends the analysis to smeared flux tubes with arbitrary profiles.

Findings

Contact term acts as magnetic moment coupling.

Wave function redefinition clarifies perturbation theory.

Applicable to flux tubes with arbitrary profiles.

Abstract

The spectrum of a charged particle coupled to Aharonov-Bohm/anyon gauge fields displays a nonanalytic behavior in the coupling constant. Within perturbation theory, this gives rise to certain singularities which can be handled by adding a repulsive contact term to the Hamiltonian. We discuss the case of smeared flux tubes with an arbitrary profile and show that the contact term can be interpreted as the coupling of a magnetic moment spinlike degree of freedom to the magnetic field inside the flux tube. We also clarify the ansatz for the redefinition of the wave function.