Abstract
We propose covariant and non-abelian generalizations of the magnetic helicity and Beltrami equation. The gauge invariance, variational principle, conserved current, energy–momentum tensor and choice of boundary conditions elucidate the subject. In particular, we prove that any extremal of the Yang–Mills action functional 14∫ΩtrFμνFμνd4x subject to the local constraint εμναβtrFμνFαβ=0 satisfies the covariant non-abelian Beltrami equation.
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