Coleman-Mandula theorem
The 1967 Sidney Coleman and Jeffrey Mandula found Coleman Mandula- Theorem is a no-go theorem (Engl.) Of the theoretical physics that in a very general assumption is based (for example, existence and nontriviality the S-matrix , not degenerate vacuum and no massless Elementary particles ). It says that any Lie algebra that contains the Poincaré group and an internal symmetry group must be a direct product of these two groups. An external (space-time) symmetry can only be combined trivially with an internal symmetry. The tensor symmetries are already maximal with the generators of the Poincaré group.
Rudolf Haag , Jan Łopuszański and Martin Sohnius were able to show in 1975 ( Haag-Łopuszański-Sohnius theorem ) that the addition of anti-commutating generators allowed the only possible, non-trivial extension of the Poincaré algebra to a so-called super algebra (see also supersymmetry ) .
literature
- Sidney Coleman and Jeffrey Mandula: All Possible Symmetries of the S Matrix . In: Physical Review . 159, No. 5, 1967, pp. 1251-1256. bibcode : 1967PhRv..159.1251C . doi : 10.1103 / PhysRev.159.1251 .