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Noether current for exchange symmetry

  1. Sep 12, 2013 #1
    In Quantum Mechanics, when we exchange identical particles the physics doesnt change. I wonder what stuff is conserved when this symmetry is demanded.
    I asked my professor but he didnt/couldnt answer. Google is no help either.
     
  2. jcsd
  3. Sep 12, 2013 #2

    DrDu

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    That's not a discrete symmetry so Noether's theorem is not applicable and there is no infinitesimal generator which is conserved.
     
  4. Sep 12, 2013 #3

    Dale

    Staff: Mentor

    I think you mean "That's not a differentiable symmetry ..."
     
  5. Sep 12, 2013 #4
    Ok got it. Thanks.
    I find this helpful too
    http://ajp.aapt.org/resource/1/ajpias/v64/i7/p840_s3?isAuthorized=no [Broken]
     
    Last edited by a moderator: May 6, 2017
  6. Sep 12, 2013 #5
    It should be possible to formulate the exchange symmetry in terms of a continuous and differentiable unitary group, by means of mixing the particles instead of exchanging them entirely. Of course you'd have to do it in a way that recovers the discrete symmetry for a certain mixing angle.

    Cheers,

    Jazz
     
  7. Sep 12, 2013 #6

    DrDu

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    Of course, thanks!
     
  8. Sep 12, 2013 #7

    DrDu

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    I remember having seen in American Journal of Physics an explicit construction of the exchange operator in terms of x and p.
     
  9. Sep 12, 2013 #8
    I would like to read that paper. Can you give the link?
     
  10. Sep 13, 2013 #9

    DrDu

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    I fear not as I no longer have access to Am J Phys.
     
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