Noether current for exchange symmetry

  • Thread starter Ravi Mohan
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  • #1
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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.
 

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  • #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.
 
  • #3
Dale
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That's not a discrete symmetry so Noether's theorem is not applicable
I think you mean "That's not a differentiable symmetry ..."
 
  • #4
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Ok got it. Thanks.
I find this helpful too
http://ajp.aapt.org/resource/1/ajpias/v64/i7/p840_s3?isAuthorized=no [Broken]
 
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  • #5
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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
 
  • #6
DrDu
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I think you mean "That's not a differentiable symmetry ..."
Of course, thanks!
 
  • #7
DrDu
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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
I remember having seen in American Journal of Physics an explicit construction of the exchange operator in terms of x and p.
 
  • #8
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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.
I would like to read that paper. Can you give the link?
 
  • #9
DrDu
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I would like to read that paper. Can you give the link?
I fear not as I no longer have access to Am J Phys.
 

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