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Léon Rosenfeld’s general theory of constrained Hamiltonian dynamics
The European Physical Journal H ( IF 0.8 ) Pub Date : 2017-01-11 , DOI: 10.1140/epjh/e2016-70042-7
Donald Salisbury , Kurt Sundermeyer

This commentary reflects on the 1930 general theory of Léon Rosenfeld dealing with phase-space constraints. We start with a short biography of Rosenfeld and his motivation for this article in the context of ideas pursued by W. Pauli, F. Klein, E. Noether. We then comment on Rosenfeld’s General Theory dealing with symmetries and constraints, symmetry generators, conservation laws and the construction of a Hamiltonian in the case of phase-space constraints. It is remarkable that he was able to derive expressions for all phase space symmetry generators without making explicit reference to the generator of time evolution. In his Applications, Rosenfeld treated the general relativistic example of Einstein-Maxwell-Dirac theory. We show, that although Rosenfeld refrained from fully applying his general findings to this example, he could have obtained the Hamiltonian. Many of Rosenfeld’s discoveries were re-developed or re-discovered by others two decades later, yet as we show there remain additional firsts that are still not recognized in the community.

中文翻译:

莱昂·罗森菲尔德(LéonRosenfeld)约束哈密顿动力学的一般理论

该评论反映了1930年LéonRosenfeld处理相空间约束的一般理论。我们从罗森菲尔德的简短传记及其在W. Pauli,F。Klein和E. Noether追求的思想的角度出发撰写本文的动机开始。然后,我们评论罗森菲尔德的通论,该通论涉及对称和约束,对称生成器,守恒律以及在相空间约束的情况下构造哈密顿量。值得注意的是,他能够导出所有相空间对称性生成器的表达式,而无需明确引用时间演化的生成器。罗森菲尔德在他的《应用》一书中处理了爱因斯坦-麦克斯韦-狄拉克理论的广义相对论例子。我们证明,尽管罗森菲尔德(Rosenfeld)并未将他的一般发现完全应用于该示例,他本可以获得哈密顿量。Rosenfeld的许多发现在二十年后被其他人重新开发或重新发现,但是正如我们所展示的那样,还有其他一些最初的发现仍未被社区认可。
更新日期:2017-01-11
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