Strong magnetic field asymptotic behaviour for the fermion-induced effective energy in the presence of a magnetic flux tube

TL;DR

This paper provides a detailed numerical analysis of the asymptotic behavior of fermion-induced effective energy in strong magnetic fields with flux tubes, clarifying previous results in 3+1 dimensions.

Contribution

It offers a detailed numerical study supporting the asymptotic formula for fermion-induced energy in strong magnetic flux tubes, clarifying previous explanations.

Findings

Numerical validation of the asymptotic formula

Clarification of the integral's behavior in strong fields

Enhanced understanding of magnetic flux tube effects

Abstract

In Ref. 3, we presented an asymptotic formula for the fermion-induced effective energy in 3+1 dimensions in the presence of a cylindrically symmetric inhomogeneous strong magnetic field. However, there are some points which were not clearly explained. In fact, the arguments, which led us to the asymptotic formula, are based on a numerical study of the integral of Eq. (10), as we will see in the main part of this paper. The aim of this work is to present this study in detail.