Chirality can be interpreted as a property of Lorentz group - Lorentz transformation of field through representation $(s, 0)$ or representation $(0, s)$. For the massless particles one says, that chirality and helicity are the same (helicity values are a chirality values multiplied by $ \hbar $). So it means, that chirality values are $\pm s$.

The questions:

1) How can I get these values for chirality? I.e., how right- and left-handed representation of the Lorentz group are connected with plus-minus signs of the chirality value?

2) Equivalence of helicity and chirality in the massless case is little not obvious for me. One uses idea that for the massless case helicity of given particle is Lorentz-invariant, the same as chirality. But it seems to me that this is not enough to identify these values. So how to identity them?

3) Also, in my previous question on the subject (Why helicity is proportional to the spin of particle and has two values?), there was a comment which give an idea of getting an answer on the question, using an equivalence of helicity and chirality. Can the helicity operator properties for massless case be given from the equivalence between helicity and chirality? Or at the beginning we get the properties of helicity operator, and only then we can identify them?


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