Proving the Spin Half Nature of Dirac Quanta

Join the discussion
Registration is free. Start your own thread to ask a follow-up.
Sign up Log in
7 replies · 3K views
quantumfireball
Messages
90
Reaction score
0
but I am confused
how do you proof that the dirac field describes spin half quanta when quantized?
please refer me to a link on the net where this derivation is shown if possible
i can't find it in any of the books on quantized field theory
 
Physics news on Phys.org

Discussion

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.
 
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
 
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.
 
blechman said:
You know that a field with N components must transform under Lorentz transformations the same way as an object with spin (N-1)/2

Not correct! spinor-vector has six components, it transforms as spin-3/2 object not 5/2.

regards

sam
 
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
 
samalkhaiat said:
blechman said:
Not correct! spinor-vector has six components, it transforms as spin-3/2 object not 5/2.

regards

sam

you're right. i was too sloppy with this comment. i retract it.

QFB: you can compute the angular momentum by studying the action of the spin operator on the field. Weinberg Vol 1 talks about this.