Generalized helicity and Beltrami fields

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 $\tfrac{1}{4}\int_Ω\tr{F_{μν}F^{μν}}\,d^4x$ subject to the local constraint $ε^{μναβ}\tr{F_{μν}F_{αβ}}=0$ satisfies the covariant non-abelian Beltrami equation.

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