unitary representation of the super Poincaré group




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The analog of unitary representation of the Poincaré group for the super Poincaré group: supersymmetry.

An irreducible representation of the super Poincaré Lie algebra is called a super multiplet. This is in general itself a super vector space which contains an ordinary irreducible unitary representation of the Poincaré group. Via the Wigner classification of fundamental particles with Poincaré irreps, this may be identified with a bosonic relativistic particle of some mass – together with the images of these “bosonic” elements under the odd generators: the superpartners of the bosonic particles.


Reviews and lecture notes include

The classification is due to

  • Werner Nahm, Supersymmetries and their representations, Nucl. Phys. B135 (1978) 149

The analogous discussion generalized to parasupersymmetry? is in

  • A. Nikitin, V. Tretynyk, Irreducible representations of the Poincaré parasuperalgebra (pdf)

Expositional slides:

  • Valerie Domcke, Supermultiplets (pdf) (in German)

Revised on March 31, 2015 13:00:59 by Urs Schreiber (