Generalized helicity and Beltrami fields

Journal Article · Thu May 15 00:00:00 EDT 2014 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/J.AOP.2014.02.014· OSTI ID:22314808

Buniy, Roman V., E-mail: [e-mail] ^[1]; Isaac Newton Institute, University of Cambridge, Cambridge, CB3 0EH ^[2]; Kephart, Thomas W., E-mail: [e-mail] ^[3]; Isaac Newton Institute, University of Cambridge, Cambridge, CB3 0EH ^[2]

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1. Schmid College of Science, Chapman University, Orange, CA 92866 (United States)
2. (United Kingdom)
3. Department of Physics and Astronomy, Vanderbilt University, Nashville, TN 37235 (United States)

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 ∫{sub Ω}trF{sub μν}F{sup μν}d{sup 4}x subject to the local constraint ε{sup μναβ}trF{sub μν}F{sub αβ}=0 satisfies the covariant non-abelian Beltrami equation. -- Highlights: •We introduce the covariant non-abelian helicity and Beltrami equation. •The Yang–Mills action and instanton term constraint lead to the Beltrami equation. •Solutions of the Beltrami equation conserve helicity.

• OSTI ID: 22314808
• Journal Information: Annals of Physics (New York), Vol. 344, Issue Complete; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ACTION INTEGRAL
BOUNDARY CONDITIONS
ENERGY-MOMENTUM TENSOR
GAUGE INVARIANCE
HELICITY
LIMITING VALUES
MATHEMATICAL SOLUTIONS
VARIATIONAL METHODS
YANG-MILLS THEORY