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.


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