Eugene Wigner showed already in 1939 that the elementary particles are
related to the irreducible representations of the Poincare 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.Comment: Lecture presented at the Poincare Symposium held in Brussels on
October 8-9, 200