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

  • $\begingroup$ Can you give some more information about your question? $\endgroup$ Jun 9, 2022 at 16:54
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    $\begingroup$ 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: en.m.wikipedia.org/wiki/Wigner%27s_theorem $\endgroup$
    – LPZ
    Jun 9, 2022 at 17:20
  • $\begingroup$ @ 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? $\endgroup$ Jun 9, 2022 at 18:18
  • $\begingroup$ See physics.stackexchange.com/q/636053/49107 $\endgroup$
    – Anyon
    Jun 11, 2022 at 15:11


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