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The identification of an electron as a particle and the positron as an antiparticle is a matter of convention. We see lots of electrons around us so they become the normal particle and the rare and unusual positrons become the antiparticle.

My question is, when you have made the choice of the electron and positron as particle and anti-particle does this automatically identify every other particle (every other fermion?) as normal or anti?

For example the proton is a particle, or rather the quarks inside are. By considering the interactions of an electron with a quark inside a proton can we find something, e.g. a conserved quantity, that naturally identifies that quark as a particle rather than an antiparticle? Or do we also just have to extend our convention so say that a proton is a particle rather than an antiparticle? To complete the family I guess the same question would apply to the neutrinos.

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Proposal : if a left-handed matter spin $\frac{1}{2}$ "entity" is part of the weak interaction, it is a particle, otherwise it is an anti-particle –  Trimok Oct 22 '13 at 17:02
I think we've seen a version of this question on the site before. Looking... –  dmckee Oct 22 '13 at 17:11
@dmckee: I've seen questions on this theme, but never a really clear answer. Trimok's comment is the closest I've seen to a definitive statement of the difference. –  John Rennie Oct 22 '13 at 17:13
@JohnRennie: re neutrinos, these would end up as particles via the lepton number; connecting to the quark sector is not as obvious, though there's (conjectired) stuff like B-L and leptoquarks –  Christoph Oct 22 '13 at 17:27
@Christoph: ah, yes, good point. –  John Rennie Oct 22 '13 at 18:22

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up vote 9 down vote accepted

Yes, to some extent. Once you choose which of the electron or positron is to be considered the normal particle, then that fixes your choice for the other leptons, because of neutrino mixing. Similarly, choosing one quark to be the normal particle fixes the choice for the other flavors and colors of quarks. But I can't think of a reason within the standard model that requires you to make corresponding choices for leptons and quarks.

In particle terms, you can think about it like this: say you start by choosing the electron to be the particle and the positron to be the antiparticle. You can then distinguish electron neutrinos and electron antineutrinos because in weak decay processes, an electron is always produced with an antineutrino and a positron with a normal neutrino. Then, because of neutrino oscillations, you can identify the other two species of neutrinos that oscillate with electron antineutrinos as antineutrinos themselves, and in turn you can identify the muon and tau lepton from production associated with their corresponding antineutrinos.

In terms of QFT, the relevant (almost-)conserved quantity is the "charge parity," the eigenvalue of the combination of operators $\mathcal{CP}$.

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Thanks. Christoph's comment made me realise that conserved lepton number automatically tells you what a neutrino is. For example in beta decay conservation of L tells you the accompanying neutrino must be an antiparticle. However I couldn't see any way to make a connection with the quarks. In SU(5)/SO(10) type models that unify leptons and quarks is there some way to link the two? Or is that a question for another day? –  John Rennie Oct 22 '13 at 19:39
I think so, since GUTs group the quarks and leptons together into unified multiplets, e.g. $(e,\nu_e,u,d)$. But I'm not personally familiar with those theories so I couldn't tell you the details. That probably would be a good topic for another question. –  David Z Oct 22 '13 at 20:00
@JohnRennie : In a $SU(5)$ model, it seems that particles and anti-particles may be mixed (if we look at the decomposition in $SU(3)*SU(2)*U(1)$), for instance the anti-symmetric representation $10$ decomposes as $10 \to (3,2,\frac{1}{6}) \oplus (3^*,1, -\frac{2}{3}) \oplus (1,1,1)$ (here all the particles/anti-particles have the same handedness). –  Trimok Oct 23 '13 at 9:35
We call particles those that compose the ordinary matter that composes us. The neutron decays to: a proton , an electron and an electron antineutrino . The paraticle identification for the electron comes from this reaction, as also the antineutrino by conservation of lepton number. –  anna v Nov 24 '13 at 8:08

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