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Is the spin statistics theorem a postulate?

  1. Apr 27, 2005 #1

    I've read one or two contradictory things about this. I was debating with a bloke recently who intensely disliked the Pauli principle, he seemed to think that something so important to the structure and stability of matter was somehow unsatisfactory if left as an ad hoc postulate. I was under the impression that spin statistics is not a postulate and was in fact derived from the relativistic version of QM. Unfortunately I won't be doing any relativistic QM, so I wonder if anyone here could tell me. Is there an explanation for spin statistics that makes sense, or is the only option the wade through the proof? (Or is it in fact a postulate?)
  2. jcsd
  3. Apr 27, 2005 #2
    There's a book on this subject: http://www.worldscibooks.com/physics/3457.html Don't know how good it is though.

    Anyway, a formal and rigorous proof requires knowledge of quanum field theory, which I don't possess, I'm afraid!
  4. Apr 28, 2005 #3
    Thanks James, I may check that book out if I ever find myself with some time.
  5. Apr 29, 2005 #4
    You can't formulate a self-consistent QFT of fermions without introducing the Pauli exclusion principle. So if we want fermions to be described by QFT (which we do, as it is one of the very few ways of formulating a theory including both relativity and quantum mechanics), we have to have the Spin-Statistics theorem. So it is kind of an assumption (we assume it to make the theory work), but it's an unavoidable one if our starting point is that they should be described by QFT.

    Of course, since both QFT and Pauli exclusion stand up extremely well to experimental tests, they are very good assumptions!
  6. Apr 29, 2005 #5
    Take a look at this thread, where we already had some discussions about that subject.

    Hope it helps :wink:

  7. Apr 29, 2005 #6

    Meir Achuz

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    The assumption in relativistic QFT has to be made that it is a local theory.
    That is sort of equivalent to what is usually thought of as point particles
    being created by the field.
    Then the spin-statistics theorum follows.
    Actually, as the early quark model showed, it is easy to circumvent the SS therom
    in practice. If color were a completely unobservable degree of freedom, then it would look like quarks were symmetrized spin 1/2 particles.
  8. Apr 30, 2005 #7


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    Ghost fields in QED,QCD & Electroweak (in SM) are virtual particles which circumvent Lüders-Pauli-Schwinger's theorem...

    (through supersymmetry transformations,called BRST symmetries).

  9. Apr 30, 2005 #8


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    Yes BRST is a little piece of supersymmetry that arises naturally in Yang-Mills theory. Would that the rest of supersymmetry were as natural!
  10. Apr 30, 2005 #9


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    Any constrained system (yes,even the free relativistic spinless particle) can be quantized BRST,even if the ghosts don't appear explicitly in the nonconstrained action.

    Really nice piece of theory,my say...

  11. Apr 30, 2005 #10
    Just wondering. Do all ghost particles need to be off mass shell and why ?
    I mean does not respecting the spin statistics automatically imply that particles are also virtual ?

  12. Apr 30, 2005 #11


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    Yes.They can't be in/out states.Not in the SM which is Poincaré invariant.

  13. May 1, 2005 #12


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    There are a few subtelties with the spin statistics theorems and loopholes around it, summarized beautifully in PCT, spin and statistics and all that by Wightman/Streater. Its quite technical and I have promptly forgotten a lot of it. But its more or less still the state of the art in terms of mathematical rigor, at least for that particular problem.
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