Spin half

1. Nov 12, 2007

quantumfireball

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. Nov 12, 2007

blechman

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.

3. Nov 12, 2007

quantumfireball

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

4. Nov 12, 2007

blechman

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.

5. Nov 12, 2007

samalkhaiat

6. Nov 12, 2007

quantumfireball

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

7. Nov 13, 2007

blechman

8. Nov 13, 2007

quantumfireball

thanks Dr Belchman