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Generalized helicity and Beltrami fields
High Energy Physics - Theory · Submitted 21 May 2013
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim 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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The abstract, sentence by sentence
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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We propose covariant and non-abelian generalizations of the magnetic helicity and Beltrami equation. | contribution 1.00 | 0.92 | 0.15 | asserted 0.95 |
| s1 | The gauge invariance, variational principle, conserved current, energy-momentum tensor and choice of boundary conditions elucidate the subject. | contribution 0.51 | 0.69 | 0.05 | asserted 0.91 |
| s2 | 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. | result 0.99 | 0.93 | 0.76 | asserted 1.00 |
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Original 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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