Coleman–Mandula theorem

The 1967 found by Sidney Coleman and Jeffrey Mandula Coleman - Mandula theorem is a no -go theorem (English ) theoretical physics, based on very general assumptions (eg, existence and non-triviality of the S- matrix, nondegenerate vacuum and no massless elementary particles). It says that every Lie algebra which contains the Poincaré group and an internal symmetry group must be a direct product of these two groups. An external ( space-time ) symmetry can therefore only be trivially combined with an internal symmetry. The latest oral symmetries are thus already maximum with the generators of the Poincare group.

Rudolf Haag Jan Lopuszanski and Martin Sohnius could show ( Haag- Lopuszanski - Sohnius theorem) in 1975, however, that the addition of anticommuting generators allowed the only possible non-trivial extension of the Poincaré algebra to a so-called super algebra (see also supersymmetry ).