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Chirality is defined through the ±1 eigenvalue under action of γ^5 on ψ, a Dirac field thus projected into its left- or right-handed component by the projection operators (1−γ^5)/2 or (1+γ^5)/2 on ψ. For massless particles (only!) chirality coincides with [helicity], a notion which is frame-dependent, and hence ambiguous for massive particles. Avoid using the [helicity] tag instead: the projectors *must* be implied.

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Conceptual interpretation of the left- and right-handed spinor representations of the Lorent...

For massive spinors "right-handed" and "left-handed" chirality isn't tied so much to true rotations, as to the casting of Lorentz transformations as "space-time rotations". … Or turning the statement on its ear, applying a parity transform changes the spinor rep, hence its chirality. …
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