Friday, August 7, 2015

mass - Mathematical proof on helicity of a massive fermion is not Lorentz invariant


What is the mathematical proof that the helicity of a massive spin-$1/2$ fermion is not Lorentz invariant?


Something is Lorentz invariant (e.g., $P_\mu P^\mu$) if it commutes with all the generators of the Lorentz group. Assuming this statement to be correct, the helicity operator, therefore, must not commute with all the generators $\frac{1}{2}\sigma_{\mu\nu}$ of Lorentz transformation. I should also be able to verify that in the limit the mass $m\to 0$, a Lorentz transformation doesn't change the helicity.


Is this line of reasoning sufficient to prove the failure of Lorentz invariance of the helicity operator?





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