Vacuum polarization by a magnetic flux of special rectangular form

TL;DR

This paper calculates the ground state energy of a spinor field in a square well magnetic flux tube using zeta-function regularization, providing a numerically suitable, renormalized expression and higher-order heat kernel coefficients.

Contribution

It introduces a method to evaluate the ground state energy in a specific magnetic flux configuration with detailed numerical and analytical techniques.

Findings

Derived a convergent integral expression for the energy

Performed numerical calculations of the energy

Calculated higher order heat kernel coefficients

Abstract

We consider the ground state energy of a spinor field in the background of a square well shaped magnetic flux tube. We use the zeta- function regularization and express the ground state energy as an integral involving the Jost function of a two dimensional scattering problem. We perform the renormalization by subtracting the contributions from first several heat kernel coefficients. The ground state energy is presented as a convergent expression suited for numerical evaluation. We discuss corresponding numerical calculations. Using the uniform asymptotic expansion of the special functions entering the Jost function we are able to calculate higher order heat kernel coefficients.