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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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What is the physical interpretation of chirality / chiral anomaly?

I'm not quite familiar with the physical context of chirality and its anomaly. What actually happens physically when an eigenvalues of the Dirac operator "flips" the sign? …