The action principle by Low (1958 Proc. R. Soc. Lond. A 248 282–7) for the classic Vlasov–Maxwell system contains a mix of Eulerian and Lagrangian variables. This renders the Noether analysis of reparametrization symmetries inconvenient, especially since the well-known energy- and momentum-conservation laws for the system are expressed in terms of Eulerian variables only. While an Euler–Poincaré formulation of Vlasov–Maxwell-type systems, effectively starting with Low’s action and using constrained variations for the Eulerian description of particle motion, has been known for a while Cendra et al (1998 J. Math. Phys. 39 3138–57), it is hard to come by a documented derivation of the related energy- and momentum-conservation laws in the spirit of the Euler–Poincaré machinery. To our knowledge only one such derivation exists in the literature so far, dealing with the so-called guiding-center Vlasov–Darwin system Sugama et al (2018 Phys. ...

中文翻译：

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局部Vlasov-Maxwell型系统的Euler-Poincaré公式中的能量和动量守恒

Low（1958 Proc。R. Soc。Lond。A 248 282-7）的经典Vlasov-Maxwell系统的作用原理包含欧拉变量和拉格朗日变量的混合。这使得Noether对重新参数化对称性的分析变得不便，特别是因为众所周知的系统能量和动量守恒定律仅以欧拉变量表示。早在Cendra等人（1998 J. Math。Phys。39 3138 –57），很难从欧拉-庞加莱机器的精神出发，通过文件证明相关的能量守恒和动量守恒定律。据我们所知，迄今为止在文献中仅存在一种推论，