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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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Does any Hamiltonian with spectrum mirrored about 0 have a sublattice/chiral symmetry?

This is a follow-up of my previous question on time reversal. Again, I don't think this should be the case, because, for one thing, supposedly we can have charge conjugation symmetry alone. Consider t …
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