Particle Physics as Representations of the Poincaré Algebra

Eugene Wigner showed already in 1939 that the elementary particles are related to the irreducible representations of the Poincaré algebra. In the light-cone frame formulation of quantum field theory one can extend these representations to depend also on a coupling constant. The representations then become non-linear and contain the interaction terms which are shown to have strong uniqueness. Extending the algebra to supersymmetry it is shown that two field theories stick out, N = 4 Yang-Mills and N = 8 Supergravity and their higher dimensional analogues. I also discuss string theory from this starting point. Lecture presented at the Poincaré Symposium held in Brussels on October 8-9, 2004 Light-Cone Field Theory 2