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        "quote": "我们讨论的主题常被称为对“<u id=\"concept-1-symmetry-group\" class=\"concept-term\" data-concept-id=\"concept-1-symmetry-group\" data-concept-role=\"discussion\" data-concept-identity=\"urn:uuid:126c82d1-85b0-4175-af2f-9d01a27e0e2e\" data-concept-route=\"/concept-identities#concept-126c82d1-85b0-4175-af2f-9d01a27e0e2e\">对称群(symmetry group)</u>”的研究，这是因为群有时会由一组变换构成：群元素作为空间 $M$ 上的变换起作用，同时保持某种特定结构（因此这些变换称为“对称变换”）。不过要强调，所讨论的变换并不一定要保持任何特定结构。在物理学应用中，“对称”一词最好只用于这样的情形：群作用于物理系统并保持运动方程不变（例如，在经典力学中使[<u class=\"concept-term\" data-concept-reference=\"concepts/quantum-mechanics/hamiltonian\" data-concept-identity=\"urn:uuid:4eb4e3f1-c861-4ad3-aa28-6972dd6ea552\" data-concept-route=\"/concept-identities#concept-4eb4e3f1-c861-4ad3-aa28-6972dd6ea552\" id=\"first-1a5f4280c9dab3c7c162-zh\">哈密顿函数(Hamiltonian function)</u>](../../../../../concepts/quantum-mechanics/hamiltonian)保持不变）。对于这类对称变换群，利用这类群的表示论推导出关于量子力学系统行为的结论，是表示论的一项重要应用。不过我们会看到，表示论在量子力学中的作用远不止于此：量子理论的整体结构由一些并非对称的群作用决定（此处“非对称”指不保持哈密顿量）。",
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