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Supergravity by Daniel Z. Freedman, Antoine Van Proeyen

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The Dirac equation is based on special representations of the Lorentz group, called spinor representations. They were discovered by Élie Cartan in 1913 [6, 7]. These representations are very different from the D-dimensional defining representation discussed in Ch. 1 (and from tensor products of the defining representation). It is remarkable and profound that spinor representations are realized in Nature and are not just mathematical curiosities. They describe fermionic particles such as the electron and quarks, and they are required for supersymmetry.

Our treatment of the Dirac equation should be viewed as part of our review of the basic notions ...

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