Coleman-Mandula theorem

The Coleman–Mandula Theorem


The Coleman–Mandula theorem is a no-go theorem motivated by the possibilities of Lie group symmetries in quantum field theory in Minkowski space-time.


Any Lie group containing the Poincaré group PP (in 4d) as a subgroup and containing a maximal internal? symmetry group GG must be a direct product of those. In addition, GG must be a semisimple Lie group with additional U(1)U(1) (circle group) factors.

The generalization of this statement to super Lie algebras is known as the Haag–Łopuszański–Sohnius theorem.


Gel’fand and Likhtman showed that with a slight extension of the concept of Lie group, one can get that PP and GG combine in a nontrivial way. This happens for example in the supersymmetric case.


  • Sidney Coleman, Jeffrey Mandula, All Possible Symmetries of the S Matrix, Physical Review 159 (5): 1251–1256 (1967)

  • I. M. Gel'fand, E. S. Likhtman, JETP Letters 13, 323 (1971)

Review includes

Revised on January 5, 2017 14:30:12 by Urs Schreiber (