Why Photon Spin on Z Direction Must be +1 or -1

[paweld]

Why photn (boson with spin 1) can have only two projections of spin on z direction +1 or -1
(0 is not allowed). Is it possible to explain this in terms of quantum mechanics or is it
only our assumptions well justified by experiment.

 

[SpectraCat]

Why photn (boson with spin 1) can have only two projections of spin on z direction +1 or -1
(0 is not allowed). Is it possible to explain this in terms of quantum mechanics or is it
only our assumptions well justified by experiment.

The photon spin projections +1 and -1 correspond to the different helicities of the photons, that is, the projection of their angular momentum on their direction of travel. The two states are equivalent to right and left circularly polarized light.

As I understand it, if a photon had a spin projection of zero on its direction of travel, then one could construct a reference frame where it was at rest. In order for this to happen, it would have to have a non-zero rest mass. This would then make it a virtual photon, which basically means that we could never detect it experimentally.

 

[bobquantum]

It is not possible to have a photon with spin zero because if it did, the the photon, at a stand still, would have no mass and therefore is basically non-existent.

 

[meopemuk]

Why photn (boson with spin 1) can have only two projections of spin on z direction +1 or -1
(0 is not allowed). Is it possible to explain this in terms of quantum mechanics or is it
only our assumptions well justified by experiment.

According to Wigner's theory, each elementary particle corresponds to an irreducible unitary representation of the Poincare group. (the best reference is S. Weinberg, "The quantum theory of fields" vol. 1) Such irreducible representations are classified by two parameters - mass and spin (or helicity). If the mass is zero then helicity can take any integer value: ...-2, -1, 0, 1, 2, ... (there are other more exotic possibilities, but they have not been seen in nature). In fact, photon is not represented by a single irreducible representation (so it is not a true elementary particle, according to Wigner). Photon is described by a direct sum of two massless irreducible representations with helicities -1 and 1. Why this is the case? Nobody knows. That's just the way it is.

Eugene.

 

[paweld]

Photon is described by a direct sum of two massless irreducible representations with helicities -1 and 1. Why this is the case? Nobody knows. That's just the way it is.

Could you explain what do you mean by helicity. Is it simply projection of the spin on direction of motion.

 

[meopemuk]

Could you explain what do you mean by helicity. Is it simply projection of the spin on direction of motion.

Operator of spin can be defined only for massive particles. For massless particles helicity is the projection of the angular momentum on the direction of motion (momentum) (\mathbf{J} \cdot \mathbf{P})/P. In the 1-photon Hilbert space this operator has only two (eigen)values: -1 and 1.

Eugene.

 

[TFT]

Because of the U(1) gauge symmetry.