nLab
unitary representation of the super Poincaré group

Context

Super-Geometry

Physics

physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes


theory (physics), model (physics)

experiment, measurement, computable physics

Contents

Idea

A super-unitary representation of the super Poincaré group (supersymmetry)

The analog in superalgebra/supergeometry of a unitary representation of the Poincaré group.

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.

References

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 November 29, 2016 15:53:49 by Urs Schreiber (89.204.135.38)