Generalized helicity and Beltrami fields

摘要

We propose Lorentz-covariant 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 Maxwell action functional 1/4∫_? _(μv)F_(μv) d~4x subject to the local constraint ε~(μvαβ)F_(μv)F_(αβ)= 0 satisfies the covariant Beltrami equation.