nLab
unitary representation of the super Poincaré group

Idea

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 super multiplet. It is in general itself a super vector space which contains an ordinary irreducible unitary representation of the Poincaré group – which 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.

Related concepts

• supersymmetry

• Wigner classification

  • unitary representation of the Poincaré group

• Doplicher-Roberts reconstruction theorem

• quantum field theory

References

A survey with precise details is

• V. Varadarajan, Unitary representations of super Lie groups (pdf)

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)