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For a quantum symmetry, is the operator of symmetry necessary to be unitary?

Milad Jangjan
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  • Can you give some more information about your question? – Brendan Darrer Jun 09 '22 at 16:54
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    More or less, it can also be anti-unitary like in the case of time reversal symmetry. You’ll need to precisely define what is a symmetry in the context of QM. Check out Wigner’s theorem for more information: https://en.m.wikipedia.org/wiki/Wigner%27s_theorem – LPZ Jun 09 '22 at 17:20
  • @ Brendan Darrer. @ lpz For example, the chiral and inverse symmetry operators are unitary, and the Time-reversal and particle-hole operators are anti-unitary. Can I say that there is symmetry such that C H C^\dagger=H with operators that is neither unitary nor anti-unitary? – Milad Jangjan Jun 09 '22 at 18:18
  • See https://physics.stackexchange.com/q/636053/49107 – Anyon Jun 11 '22 at 15:11

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