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I Invariance of an observable A

  1. Jan 26, 2017 #1
    How do I know if an observable is invariant, specifically under some set of transformations described via the generators ##G_i##? Which conditions would this observable have to fulfil?
     
  2. jcsd
  3. Jan 26, 2017 #2

    dextercioby

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    How is the observable defined? Can it be written in terms of Gi?
     
  4. Jan 26, 2017 #3
    It's just a quantum mechanical observable, A. I have no more information than that about it. I'm not sure what ##G_i## is, so I'm not sure if it can be written like that. Strange question really, can't seem to find the answer on google. :)
     
    Last edited: Jan 26, 2017
  5. Jan 26, 2017 #4
    Apparently the answer is that the observable must commute. With what exactly I don't know, but there we are!
     
  6. Jan 27, 2017 #5

    strangerep

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    The observable is represented as an operator "##A##" (say) on Hilbert space. The symmetry generators ##G_i## are represented as operators on the same Hilbert space. The notion that the observable is invariant under those symmetries is implemented by requiring ##[A, G_i] = 0##. I.e., the observable operator must commute with the symmetry generators.

    My only other suggestion is: "get thee to a copy of Ballentine" (quickly). :oldbiggrin:
     
  7. Jan 28, 2017 #6
    Yeah, good plan. Quite a lot of textbooks needed, I think. Thanks for your help! :)
     
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