Zero modes in finite range magnetic fields

TL;DR

This paper discovers a class of Fermion zero modes in three-dimensional space for Abelian Dirac operators, where magnetic fields are confined to a finite region, advancing understanding of localized quantum states.

Contribution

It introduces a new class of zero modes with finite-range magnetic fields, expanding the theoretical framework of Dirac operators in finite regions.

Findings

Zero modes exist with magnetic fields confined to finite regions.

The gauge potentials are nonzero only within a bounded space.

This work broadens the understanding of localized fermionic states.

Abstract

We find a class of Fermion zero modes of Abelian Dirac operators in three dimensional Euclidean space where the gauge potentials and the related magnetic fields are nonzero only in a finite space region.