关于Noether定理——分析力学札记之三十

德国女数学家Noether E于1918年发表重要论文“不变变分问题”。这篇论文给出两个定理,第一定理涉及经典力学的对称性与守恒量,第二定理涉及广义相对论。Noether第一定理不仅已成为研究经典力学和经典场论中,而且已成为研究量子力学和量子场论中对称性与守恒量关系的基础。本文介绍了Noether的这篇论文和她思想的传播,以及经典力学中的Noether定理。

ON THE NOETHER’S THEOREM1)

Emmy Noether, German female mathematician, published in 1918 an important paper, entitled "On Invariant Functionals", in which two theorems are proved. The first theorem is about the symmetries and the invariants in classical mechanics; the second theorem is about the general relativity. Noether's first theorem is now a basis not only for classical mechanics and classical field theory, but also for the studies of symmetries and invariants in quantum mechanics and quantum field theory. This paper gives an introduction to her paper and the development her ideas, as well as the Noether's theorem in classical mechanics.