### 抄録

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.

元の言語 | 英語 |
---|---|

記事番号 | 465501 |

ジャーナル | Journal of Physics A: Mathematical and Theoretical |

巻 | 47 |

発行部数 | 46 |

DOI | |

出版物ステータス | 出版済み - 11 21 2014 |

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### All Science Journal Classification (ASJC) codes

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

### これを引用

*Journal of Physics A: Mathematical and Theoretical*,

*47*(46), [465501]. https://doi.org/10.1088/1751-8113/47/46/465501

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

研究成果: ジャーナルへの寄稿 › 記事

*Journal of Physics A: Mathematical and Theoretical*, 巻. 47, 番号 46, 465501. https://doi.org/10.1088/1751-8113/47/46/465501

}

TY - JOUR

T1 - Relabeling symmetry in relativistic fluids and plasmas

AU - Kawazura, Yohei

AU - Yoshida, Zensho

AU - Fukumoto, Yasuhide

PY - 2014/11/21

Y1 - 2014/11/21

N2 - 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.

AB - 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.

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UR - http://www.scopus.com/inward/citedby.url?scp=84909961805&partnerID=8YFLogxK

U2 - 10.1088/1751-8113/47/46/465501

DO - 10.1088/1751-8113/47/46/465501

M3 - Article

AN - SCOPUS:84909961805

VL - 47

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 46

M1 - 465501

ER -