The ground state energy of a spinor field in the background of a finite radius flux tube

TL;DR

This paper develops a formalism to calculate the ground state energy of a spinor field in a cylindrically symmetric magnetic background, applying it to a finite radius flux tube and numerically analyzing the energy dependence on physical parameters.

Contribution

It introduces a new formalism using the Jost function and asymptotic expansions to evaluate the ground state energy in magnetic flux tube backgrounds.

Findings

Ground state energy is negative and smaller than classical energy for most parameters.

The energy remains below classical energy except at very small radii.

Numerical results depend on the flux and radius of the flux tube.

Abstract

We develop a formalism for the calculation of the ground state energy of a spinor field in the background of a cylindrically symmetric magnetic field. The energy is expressed in terms of the Jost function of the associated scattering problem. Uniform asymptotic expansions needed are obtained from the Lippmann-Schwinger equation. The general results derived are applied to the background of a finite radius flux tube with a homogeneous magnetic field inside and the ground state energy is calculated numerically as a function of the radius and the flux. It turns out to be negative, remaining smaller by a factor of $\alpha$ than the classical energy of the background except for very small values of the radius which are outside the range of applicability of QED.