Proving the Spin Half Nature of Dirac Quanta

In summary, the Dirac field can be shown to describe spin half quanta when quantized by taking the nonrelativistic limit of the Dirac equation and recovering the spin-term in the hamiltonian. This is supported by the Spin-Statistics Theorem which states that fermions must have half-integer spin. Other fields with different spin values can be determined by counting the number of polarization states and studying the action of the spin operator on the field. Weinberg's Quantum Field Theory textbook covers this topic in more detail.
  • #1
quantumfireball
91
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
 
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  • #2
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
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
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
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
 
  • #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
 
  • #7
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.
 
  • #8
thanks Dr Belchman
 

1. What is the Spin Half Nature of Dirac Quanta?

The Spin Half Nature of Dirac Quanta refers to the quantum mechanical property of particles described by the Dirac equation to have a spin of 1/2. This spin is a fundamental property of particles and is a measure of their intrinsic angular momentum.

2. Why is it important to prove the Spin Half Nature of Dirac Quanta?

Proving the Spin Half Nature of Dirac Quanta is important because it helps us understand the fundamental nature of matter and how particles behave at the quantum level. It also has important implications in fields such as particle physics and quantum computing.

3. How was the Spin Half Nature of Dirac Quanta first discovered?

The Spin Half Nature of Dirac Quanta was first discovered by physicist Paul Dirac in the 1920s while trying to reconcile quantum mechanics with special relativity. He found that his equation predicted the existence of particles with a spin of 1/2, which was later confirmed by experiments.

4. What evidence supports the Spin Half Nature of Dirac Quanta?

There is a significant amount of experimental evidence that supports the Spin Half Nature of Dirac Quanta. This includes observations of the spin of particles in particle accelerators, measurements of the magnetic moments of particles, and the behavior of particles in magnetic fields.

5. Are there any alternative theories to the Spin Half Nature of Dirac Quanta?

Currently, there are no alternative theories that can fully explain the Spin Half Nature of Dirac Quanta. However, there are ongoing efforts to develop new theories, such as supersymmetry, that could potentially provide a different explanation for this phenomenon.

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