别名：wavefunctions
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Woit · 2025-10-20
已登记出处中的最早位置：§1.4 · zh-CN。
来源短摘录与定位
§1.4 · zh-CN · translation · unreviewed
构造量子力学态空间 的一种方式，是把态表示为“波函数(wavefunction)”，也就是定义在时空上的复值函数。给定时空上的任意群作用，依照方程 (1.3) 的构造，便可在这类波函数组成的态空间 上得到表示 。然而，我们感兴趣的许多表示并非由这种构造得到。接下来几章将先研究这类更简单的有限维例子；之后再讨论由时空上的群作用诱导的无限维表示。
§1.4 · en · original_transcription · ai-transcription-compared
One way to construct quantum mechanical state spaces is as “wavefunctions”, meaning complex-valued functions on space-time. Given any group action on space-time, we get a representation on the state space of such wavefunctions by the construction of equation 1.3. Many of the representations of interest will however not come from this construction, and we will begin our study of the subject in the next few chapters with such examples, which are simpler because they are finite dimensional. In later chapters we will turn to representations induced from group actions on space-time, which will be infinite dimensional.