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 1/4 f(Omega) trF(mu nu) F-mu nu d(4)x subject to the local constraint epsilon(mu nu alpha beta)trF(mu nu)F(alpha beta) = 0 satisfies the covariant non-abelian Beltrami equation.
Buniy, Roman V., and Thomas W. Kephart. "Generalized helicity and Beltrami fields." Annals of Physics 344 (2014): 179-193. doi: 10.1016/j.aop.2014.02.014
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NOTICE: this is an earlier version of a work that was accepted for publication in Annals of Physics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Annals of Physics, volume 344, in 2014. DOI: 10.1016/j.aop.2014.02.014
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