Projecting a non-Abelian $\mathrm{SU}\left(2\right)\mathrm{}$ 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.

• Received 15 November 1999

DOI:https://doi.org/10.1103/PhysRevD.61.105015