标题： 对称性的研究：一些通用技术 显示英文标题

标题： The study of symmetries: some general techniques

摘要： 设$S(H)$为$H$上所有自伴有界线性算子的集合，$\mathcal{V} \subset S(H)$是在量子力学数学基础中相关的一个子集。对称性是一个双射映射$\phi :\mathcal{V} \to \mathcal{V}$，它相对于$\mathcal{V}$上一个或多个在数学物理中有意义的关系和/或运算而言是一个自同构。我们将解释当研究对称性的普遍形式时可以使用的一些想法。 显示英文摘要

摘要： Let $S(H)$ be the set of all self-adjoint bonded linear operators on $H$ and $\mathcal{V} \subset S(H)$ a subset that is pertinent in mathematical foundations of quantum mechanics. A symmetry is a bijective map $\phi :\mathcal{V} \to \mathcal{V}$ which is an automorphism with respect to one or more relations and/or operations on $\mathcal{V}$ that are relevant in mathematical physics. We will explain several ideas that can be used when studying the general form of symmetries.