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I have a question about majorana neutrinos.

Majorana particles are particles that are their own antiparticle. From this I would argue that they need to have all quantum numbers equal to zero. My question is: what about the weak isospin? This cannot be zero, as neutrinos partecipate into weak interactions.

Thank you for any help on this.

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You say about Majorana fermions:

"From this I would argue that they need to have all quantum numbers equal to zero."

which is not true. Charge conjugation is defined on Dirac spinors as $\psi^c := \mathrm{i}\gamma^0\gamma^2\bar\psi^T$. Being Majorana means $\psi^c = \psi$. While this would imply the spinor has zero electric charge (and zero all other $\mathrm{U}(1)$ charges, if there were any, probably), this does not imply anything about the representations of the other gauge groups it transforms in.

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  • $\begingroup$ The notion that antiparticles "have all quantum numbers flipped" is an oversimplification. $\endgroup$ – Ryan Unger Mar 6 '15 at 20:34
  • $\begingroup$ Under the standard seesaw mechanism, doesn't "Majorana neutrinos" mean not Majorana bispinors satisfying $\Psi^c = \Psi$, but instead Dirac spinors (which transform nontrivially under charge conjugation) with Majorana mass terms? $\endgroup$ – tparker Apr 11 '20 at 20:49

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