The subject we are considering is often described as the study of “symmetry groups”, since the groups may occur as groups of elements acting by transformations of a space preserving some particular structure (thus, a “symmetry transformation”). We would like to emphasize though that it is not necessary that the transformations under consideration preserve any particular structure. In the applications to physics, the term “symmetry” is best restricted to the case of groups acting on a physical system in a way that preserves the equations of motion (for example, by leaving the Hamiltonian function unchanged in the case of a classical mechanical system). For the case of groups of such symmetry transformations, the use of the representation theory of the group to derive implications for the behavior of a quantum mechanical system is an important application of the theory. We will see however that the role of representation theory in quantum mechanics is quite a bit deeper than this, with the overall structure of the theory determined by group actions that are not symmetries (in the sense of not preserving the Hamiltonian).
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正文：英文 · 原著转录
核对状态：AI 辅助转录核对，未作人工审阅
原书 PDF · 印刷页 11
来源版本：2025-10-20
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