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Weyl spinors are not eigenstates of the helicity operator when the mass is not zero.
But they have well-defined chiralities no matter what the mass is.
Yet, it seems to me that references keep talking of Weyl spinors as if they have well-defined helicities, regardless of the mass.
First, people keep talking of the Weyl spinors as left-handed and right-handed, even when there is a mass present. I guess that they are really talking about the chirality here, even though they use the language of handedness. Am I correct?
Second, consider CPT. I have read that the CPT conjugate of a left-handed spinor is the right-handed antiparticle state. It seems to me here again that we are trully talking about chirality, not helicity. And yet I have read some authors saying that CPT conjugates have opposite helicities.
Third, consider Lorentz boosts. Now it definitely seem that under a Lorentz boost, we may change a positive helicity state into a negative helicity state. But that does not imply that we are transforming a left-handed Weyl spinor into a right-handed Weyl spinor, since these do not have well-defined helicities. And yet, that seems to be what is implied by some authors.
Anyoen can shed some light on these points?
Thanks!
Patrick
But they have well-defined chiralities no matter what the mass is.
Yet, it seems to me that references keep talking of Weyl spinors as if they have well-defined helicities, regardless of the mass.
First, people keep talking of the Weyl spinors as left-handed and right-handed, even when there is a mass present. I guess that they are really talking about the chirality here, even though they use the language of handedness. Am I correct?
Second, consider CPT. I have read that the CPT conjugate of a left-handed spinor is the right-handed antiparticle state. It seems to me here again that we are trully talking about chirality, not helicity. And yet I have read some authors saying that CPT conjugates have opposite helicities.
Third, consider Lorentz boosts. Now it definitely seem that under a Lorentz boost, we may change a positive helicity state into a negative helicity state. But that does not imply that we are transforming a left-handed Weyl spinor into a right-handed Weyl spinor, since these do not have well-defined helicities. And yet, that seems to be what is implied by some authors.
Anyoen can shed some light on these points?
Thanks!
Patrick