nLab
Coleman-Mandula theorem

The Coleman–Mandula Theorem

Idea

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.

Statement

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.

Remarks

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.

References

  • 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 (147.231.89.7)