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arXiv · 1305.4927

Generalized helicity and Beltrami fields

Roman V. Buniy·Thomas W. Kephart
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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 $\tfrac{1}{4}\int_\Omega\tr{F_{\mu\nu}F^{\mu\nu}}\,d^4x$ subject to the local constraint $\epsilon^{\mu\nu\alpha\beta}\tr{F_{\mu\nu}F_{\alpha\beta}}=0$ satisfies the covariant non-abelian Beltrami equation.

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Roman V. Buniy, Thomas W. Kephart. 2013-05-21. Generalized helicity and Beltrami fields. https://doi.org/10.1016/j.aop.2014.02.014

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