Wigner's theorem | Wikipedia audio article
Channel: wikipedia tts
Date: 2018-12-28

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Wigner%27s_theorem


00:00:51 1 Rays and ray space
00:09:18 2 Symmetry transformations
00:14:59 3 Symmetry groups
00:16:37 4 Statement of Wigner's theorem
00:16:47 4.1 Preliminaries
00:22:33 4.2 Statement
00:24:12 5 Representations and projective representations
00:26:34 5.1 Utility of phase freedom
00:36:19 6 See also
00:36:58 7 Remarks
00:39:33 8 Notes
00:39:47 9 References



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SUMMARY
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Wigner's theorem, proved by Eugene Wigner in 1931,  is a cornerstone of the mathematical formulation of quantum mechanics. The theorem specifies how physical symmetries such as rotations, translations, and CPT are represented on the Hilbert space of states.
According to the theorem, any symmetry transformation of ray space is represented by a linear and unitary or antilinear and antiunitary transformation of Hilbert space. The representation of a symmetry group on Hilbert space is either an ordinary representation or a projective representation.