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According to "Supersymmetry in Particle Physics" by Ian Aitchison (see e.g. p62 of arXiv), in the Minimal Supersymmetric Standard Model (MSSM) we can use Majorana language to build supermultiplets:

[There is] a possible alternative formalism, in which one uses 4-component Majorana spinor fields (see section 2.3) rather than the 2-component L-or R-spinor fields we have been using up till now

But a Majorana spinor is its own charge conjugate. So, how do we assign a Majorana spinor to a charged particle, say the electron?

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  • $\begingroup$ Are you sure it doesn't say Weyl spinors? A Weyl spinors 2 on shell degrees of freedom match the 2 dof of a complex scalar. $\endgroup$
    – innisfree
    Commented Dec 2, 2015 at 10:22
  • $\begingroup$ They start building a Lagrangian in Weyl form, then switch to Majorana form. First mention of this was on page 77 (Wess-Zumino model). I can see how Weyl and Majorana languages are equivalent, but i'm confused in the assignment of particles and antiparticles, R-types and L-types. $\endgroup$
    – Kosm
    Commented Dec 2, 2015 at 10:36
  • $\begingroup$ Oh, sorry, different version of the book. In this version it's page 62. $\endgroup$
    – Kosm
    Commented Dec 2, 2015 at 10:45
  • $\begingroup$ Oh hang on. He probably just means you can put the 2-component Weyl spinor into a 4 component (but 2 dof) Majorana spinor. Weyl spinors are the natural choice in SUSY though. $\endgroup$
    – innisfree
    Commented Dec 2, 2015 at 10:45
  • $\begingroup$ Then you'd have a Majorana spinor for the LH electron and one for the RH electron. Giving 4 dof in total if course. $\endgroup$
    – innisfree
    Commented Dec 2, 2015 at 10:46

1 Answer 1

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Sorry this is coming so late. The answer is actually quite simple.

The reason we say Majorana spinors can't have charges is that if they did, the Majorana mass term would not be gauge invariant. In Aitchison's book, and in a number of other books on the subject, we are considering only massless spinors; the mass is added in later by the Higgs mechanism. So these "Majorana spinors" are not really Majorana at all, they're just a repackaging of the content of a Weyl spinor. Such spinors may be charged.

Describing this in terms of charge conjugation is a bit confusing. I wrote an exhaustive answer here with all the details.

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