Relabeling symmetry in relativistic fluids and plasmas

Yohei Kawazura, Zensho Yoshida, Yasuhide Fukumoto

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

The conservation of the recently formulated relativistic canonical helicity (Yoshida et al 2014 J. Math. Phys. 55 043101) is derived from Noether's theorem by constructing an action principle on the relativistic Lagrangian coordinates (we obtain general cross helicities that include the helicity of the canonical vorticity). The conservation law is, then, explained by the relabeling symmetry pertinent to the Lagrangian label of fluid elements. Upon Eulerianizing the Noether current, the purely spatial volume integral on the Lagrangian coordinates is mapped to a space-time mixed three-dimensional integral on the four-dimensional Eulerian coordinates. The relativistic conservation law in the Eulerian coordinates is no longer represented by any divergence-free current; hence, it is not adequate to regard the relativistic helicity (represented by the Eulerian variables) as a Noether charge, and this stands the reason why the 'conventional helicity' is no longer a constant of motion. We have also formulated a relativistic action principle of magnetohydrodynamics (MHD) on the Lagrangian coordinates, and have derived the relativistic MHD cross helicity.

Original languageEnglish
Article number465501
JournalJournal of Physics A: Mathematical and Theoretical
Volume47
Issue number46
DOIs
Publication statusPublished - Nov 21 2014

Fingerprint

Helicity
Conservation
Plasma
Magnetohydrodynamics
Lagrangian Coordinates
Plasmas
Symmetry
Fluid
Fluids
fluids
symmetry
conservation laws
Noether
magnetohydrodynamics
Vorticity
Conservation Laws
Labels
Noether's theorem
Divergence-free
vorticity

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modelling and Simulation
  • Mathematical Physics
  • Physics and Astronomy(all)

Cite this

Relabeling symmetry in relativistic fluids and plasmas. / Kawazura, Yohei; Yoshida, Zensho; Fukumoto, Yasuhide.

In: Journal of Physics A: Mathematical and Theoretical, Vol. 47, No. 46, 465501, 21.11.2014.

Research output: Contribution to journalArticle

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