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I know left handed electrons and electron neutrinos are isospin doublets. Is there any analogous way in which an electron and a positron are related? My first thought is some sort time-parity doublet.

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    $\begingroup$ In a Dirac spinor, two of the four components describe the particle and the other two describe the antiparticle. $\endgroup$ – G. Smith Jun 24 at 1:54
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    $\begingroup$ Yes, you can look at the outer automorphisms of the Lorentz group, they are "doublets" under CPT. One does not need Dirac spinors for that, already a Weyl fermion transforms under these transformations. Since this is a $\mathbb{Z}_2$, not many would call this a "doublet", though. $\endgroup$ – user178876 Jun 24 at 1:58

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