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Generalized Helicity And Beltrami Fields, Roman V. Buniy, Thomas W. Kephart
Generalized Helicity And Beltrami Fields, Roman V. Buniy, Thomas W. Kephart
Mathematics, Physics, and Computer Science Faculty Articles and Research
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.