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In particle physics, helicity is the projection of the angular momentum onto the direction of momentum. For massless spin-1⁄2 particles, helicity is equivalent to the chirality operator multiplied by $\hbar/2$, so may be used for related chirality questions as well.
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Why is helicity a good quantum number while spin isn't?
I'm studying the Dirac equation for free particles and read that spin doesn't commute with the hamiltonian and one has to define the helicity operator to find a third good quantum number. …