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Title: Generalized helicity and Beltrami fields

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.
Authors:
 [1] ;  [2] ;  [3] ;  [2]
  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)
Publication Date:
OSTI Identifier:
22314808
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics (New York); Journal Volume: 344; Journal 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)
Country of Publication:
United States
Language:
English
Subject:
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