The symmetries of the Dirac--Pauli equation in two and three dimensions

TL;DR

This paper systematically determines all symmetries of the Dirac-Pauli equation in 2D and 3D, and explores zero mode degeneracy by explicitly constructing multiple zero modes and their gauge potentials.

Contribution

It provides a complete symmetry classification of the Dirac-Pauli equation in two and three dimensions and explicitly constructs zero modes with gauge potentials, advancing understanding of zero mode degeneracy.

Findings

All symmetries of the Dirac-Pauli equation in 2D and 3D are identified.

Explicit constructions of multiple zero modes with gauge potentials are provided.

Insights into zero mode degeneracy are gained through symmetry analysis.

Abstract

We calculate all symmetries of the Dirac-Pauli equation in two-dimensional and three-dimensional Euclidean space. Further, we use our results for an investigation of the issue of zero mode degeneracy. We construct explicitly a class of multiple zero modes with their gauge potentials.