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Is it the case that chirality is an intrinsic property of elementary fermions? I mean, is it the case that all electrons have left handed chirality while all positrons have right handed chirality? And is it possible to measure the chirality of a particle?

  • Related/possible duplicate: https://physics.stackexchange.com/q/246637/50583, https://physics.stackexchange.com/q/161170/50583 – ACuriousMind May 07 '17 at 15:04

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No, massive particles necessarily have components corresponding to both left-handed and right-handed chirality. "Only left-handed fermions and right-handed antifermions interact with the weak interaction", but right-handed Fermions do exist and chirality can change dynamically.

Regarding measurability, see this question.

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