Generalized helicity and Beltrami fields

Tangled Magnetic Fields in Astro- and Plasma Physics; Quantised Flux in Tightly Knotted and Linked Systems

Buniy, Roman V.^1 ; Kephart, Thomas W.^2

Schmid College of Science, Chapman University, Orange

CA

92866, United States^1

Department of Physics and Astronomy, Vanderbilt University, Nashville

TN

37235, United States^2

关键词: Action functional;    Beltrami equation;    Beltrami fields;    Energy-momentum tensor;    Gauge invariance;    Local constraints;    Magnetic helicity;    Variational principles;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/544/1/012008/pdf
DOI  :  10.1088/1742-6596/544/1/012008

来源: IOP

【 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 1/2 ∫ΩFμvFμvd4x subject to the local constraintμvαβFμvFαβ 0 satisfies the covariant Beltrami equation.