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Spin half

  1. Nov 12, 2007 #1
    but im confused
    how do you proof that the dirac field describes spin half quanta when quantized???
    plz refer me to a link on the net where this derivation is shown if possible
    i cant find it in any of the books on quantized field theory
     
  2. jcsd
  3. Nov 12, 2007 #2

    blechman

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    One way you can do it is to take the nonrelativistic limit of the Dirac equation and recover the spin-term in the hamiltonian. then you'll see explicitly that it's s=1/2. see any text on relativistic QM.

    In QFT, you usually go the other way around: assume that it's a fermion and you get the Dirac equation. Fermions have to have half-integer spin thanks to the famous "Spin-Statistics Theorem". I believe this was proved first by Pauli, but I'm not sure. I'm sure Weinberg does it in his QFT tome.
     
  4. Nov 12, 2007 #3
    well what about spin a1 fields,spin 3-2 fields,spin 2 fields
    how does one go about showing that they describe quanta of that much amount of intrinsic angular momenta
     
  5. Nov 12, 2007 #4

    blechman

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    count the number of polarization states (this follows from the field equations); that tells you how many components the field has. You know that a field with N components must transform under Lorentz transformations the same way as an object with spin (N-1)/2 - this is just ordinary quantum mechanics.
     
  6. Nov 12, 2007 #5

    samalkhaiat

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  7. Nov 12, 2007 #6
    but how to show it using quantum field theory?????
    that is in terms of an operator which acts on a fock space having eigenvalue=sqrt(s(s+1))
    times the number of quanta in the fock space
    im totally confused
     
  8. Nov 13, 2007 #7

    blechman

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  9. Nov 13, 2007 #8
    thanks Dr Belchman
     
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