Continuous Spin Representations of the Poincaré and Super-Poincaré Groups

Details Continuous Spin Representations of the Poincaré and Super-Poincaré Groups Continuous Spin Representations of the Poincaré and Super-Poincaré Groups

2002-05-15

arxiv.org/abs/hep-th/0205145v1

J.Math.Phys. 43 (2002) 6279

Physics

High Energy Physics

High Energy Physics - Theory

19 pages

Scientific paper

10.1063/1.1518138

We construct Wigner's continuous spin representations of the Poincar\'e algebra for massless particles in higher dimensions. The states are labeled both by the length of a space-like translation vector and the Dynkin indices of the {\it short little group} $SO(d-3)$, where $d$ is the space-time dimension. Continuous spin representations are in one-to-one correspondence with representations of the short little group. We also demonstrate how combinations of the bosonic and fermionic representations form supermultiplets of the super-Poincar\'e algebra. If the light-cone translations are nilpotent, these representations become finite dimensional, but contain zero or negative norm states, and their supersymmetry algebra contains a central charge in four dimensions.

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