维格纳定理 Wigner's theorem
（重定向自Wigner theorem）
维格纳定理（Wigner's theorem）是由尤金·维格纳在1931年证明的，这个定理是量子力学的数学表述的奠基石。这个定理描述的是系统的对称性 (物理学)，即例如旋转，平移或者CPT这些操作是如何改变希尔伯特空间上的态。
根据这个定理，任何对称性操作都是希尔伯特空间上的一个幺正变换或者反幺正变换。更准确的说，这个定理描述的是在一个复的希尔伯特空间
上，如果对任意的
都有满射
使得
则对任意的
该满射可以被改写成如下形式
其中
的 模 为1，而
是幺正或者反幺正的。
![E.P. Wigner (1902-1995), F.R.S., first proved the theorem bearing his name. It was a key step towards the modern classification scheme of particle types, according to which particle types are partly characterized by which representation of the Lorentz group under which it transforms. The Lorentz group is a symmetry group of every relativistic quantum field theory.
Wigner early work laid the ground for what many physicists came to call the group theory disease[1] in quantum mechanics – or as Hermann Weyl (co-responsible) puts it in his The Theory of Groups and Quantum Mechanics (preface to 2nd ed.),](/uploads/202502/21/Wigner3705.jpg)