Relabeling symmetry in relativistic fluids and plasmas
Relabeling symmetry in relativistic fluids and plasmas
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重新标记相对论流体和等离子体中的对称性
DOI：
10.1088/1751-8113/47/46/465501
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
and Y. Fukumoto
中科院分区：
文献类型：
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作者：
Y. Kawazura;Z. Yoshida;and Y. Fukumoto
最近表述的相对论正则螺旋度守恒(Yoshida et al . 2014 J. Math。通过在相对论拉格朗日坐标系上构造一个作用原理（我们得到了包括正则涡度的螺旋度的一般交叉螺旋度），推导出了Noether定理。因此，守恒定律可以用与流体元素的拉格朗日标记相关的重新标记对称性来解释。将诺特电流欧拉化后，将拉格朗日坐标上的纯空间体积积分映射为四维欧拉坐标上的时空混合三维积分。欧拉坐标系中的相对论守恒定律不再由任何无散度电流表示；因此，把相对论的螺旋度（由欧拉变量表示）看作诺特电荷是不充分的，这就是为什么“常规螺旋度”不再是运动常数的原因。我们还在拉格朗日坐标系上建立了相对论性磁流体动力学的作用原理，并推导了相对论性磁流体动力学的交叉螺旋度。
The conservation of the recently formulated relativistic canonical helicity (Yoshida et al 2014 J. Math. Phys. 55 043101) is derived from Noetherʼs 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.