Relabeling symmetry in relativistic fluids and plasmas

The conservation of the recently formulated relativistic canonical helicity\footnote{Z. Yoshida, Y. Kawazura, and T. Yokoyama, J. Math. Phys. \textbf{55} 043101 (2014).}$^,$\footnote{Y. Kawazura, Z. Yoshida and Y. Fukumoto, arXiv:1405.3544 [math-p.plasm-ph]} is derived from Noether's theorem with the fluid elements' relabeling symmetry. 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. We have also formulated a relativistic action principle of MHD on the Lagrangian coordinates, and have derived the relativistic MHD cross helicity.