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arXiv 1405.3544physics.plasm-ph
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相对论性流体和等离子体中的重标记对称性

Relabeling symmetry in relativistic fluids and plasmas

Yohei Kawazura, Zensho Yoshida, Yasuhide Fukumoto

摘要:

最近制定的相对论正则螺旋度的守恒[Yoshida Z,Kawazura Y,and Yokoyama T 2014 J. Math. Phys. 55 043101]是通过在相对论拉格朗日坐标上构建作用原理从Noether定理导出的(我们获得了包括正则涡度的螺旋度的一般交叉螺旋度)。守恒定律,然后,解释了重新标记对称性有关的拉格朗日标签的流体元素。在欧拉化的诺特电流,纯粹的空间体积积分的拉格朗日坐标映射到四维欧拉坐标上的时空混合的三维积分。欧拉坐标系中的相对论性守恒定律不再由任何无发散流表示;因此,将相对论性螺旋度(由欧拉变量表示)视为诺特荷是不够的,这就是为什么“常规螺旋度”不再是运动常数的原因。在拉格朗日坐标系下建立了相对论性磁流体作用原理,导出了相对论性磁流体交叉螺旋度。

英文摘要:

The conservation of the recently formulated relativistic canonical helicity [Yoshida Z, Kawazura Y, and Yokoyama T 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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