Theorem

Coleman-Mandula Theorem

Mathematical Physics

The Coleman-Mandula Theorem states that, under general assumptions satisfied by realistic particle-physics models, the largest possible symmetry group combining spacetime symmetries with internal symmetries acting on a nontrivial interacting quantum field theory must be a simple product of the two, with no nontrivial mixing between them. Named for Sidney Coleman and Jeffrey Mandula, it was long read as ruling out any deeper unification of spacetime and internal symmetry, until the later discovery that supersymmetry evades the theorem by relying on generators that anticommute rather than commute.

Facts

Statement

The symmetry group of such a theory is necessarily a direct product of the Poincare group and an internal symmetry group. 1

Proof Year

1967 1

Classification

Statement Form

Impossibility Theorem 1

Sources

1. Coleman-Mandula theorem (Wikipedia)

Introduction
the symmetry group of this theory is necessarily a direct product of the Poincaré group and an internal symmetry group.
Opening paragraph
It is named after Sidney Coleman and Jeffrey Mandula who proved it in 1967 as the culmination of a series of increasingly generalized no-go theorems investigating how internal symmetries can be combined with spacetime symmetries.

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Coleman-Mandula Theorem