### 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 language | English |
---|---|

Article number | 465501 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 47 |

Issue number | 46 |

DOIs | |

Publication status | Published - Nov 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)

### Cite this

*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.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and Theoretical*, vol. 47, no. 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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U2 - 10.1088/1751-8113/47/46/465501

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

M3 - Article

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 -