# nLab Coleman-Mandula theorem

The ColemanMandula 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 $P$ (in 4d) as a subgroup and containing a maximal internal symmetry group $G$ must be a direct product of those. In addition, $G$ must be a semisimple Lie group with additional $U(1)$ (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 $P$ and $G$ combine in a nontrivial way. This happens for example in the supersymmetric case.

## References

Review includes

Last revised on May 11, 2022 at 07:35:41. See the history of this page for a list of all contributions to it.