Creation and evolution of magnetic helicity

TL;DR

This paper explores how magnetic helicity, derived from a non-Abelian SU(2) gauge field, relates to the winding number of the gauge group element and its evolution over time.

Contribution

It demonstrates the connection between magnetic helicity and the winding number in non-Abelian gauge fields and analyzes its non-conservation during Maxwell evolution.

Findings

Magnetic helicity equals the winding number of the gauge group element.

Helicity is not conserved but retains half its initial value at infinite time.

Projection onto electromagnetic direction yields a nontrivial magnetic field.

Abstract

Projecting a non-Abelian SU(2) vacuum gauge field - a pure gauge constructed from the group element U - onto a fixed (electromagnetic) direction in isospace gives rise to a nontrivial magnetic field, with nonvanishing magnetic helicity, which coincides with the winding number of U. Although the helicity is not conserved under Maxwell (vacuum) evolution, it retains one-half its initial value at infinite time.