Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 307 / 1 / a

The Coleman–Mandula theorem says that, under its assumptions on a nontrivial analytic relativistic S-matrix and the particle spectrum, every continuous bosonic symmetry algebra is a direct sum of the Poincare algebra and an internal symmetry algebra. Supersymmetry becomes possible by weakening the assumption that the symmetry algebra is an ordinary Lie algebra: a Z2-graded Lie superalgebra admits odd generators whose bracket is an anticommutator. The Haag–Łopuszański–Sohnius theorem then classifies the allowed extension and leads to the Super-Poincaré algebra.