Coleman–Mandula theorem

E573373

no-go theorem result in quantum field theory theorem in theoretical physics

The Coleman–Mandula theorem is a foundational result in theoretical physics that severely restricts how spacetime and internal symmetries can be combined in a unified quantum field theory, showing that only a direct product of these symmetries is generally allowed.

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Statements (45)

Predicate	Object
instanceOf	no-go theorem ⓘ result in quantum field theory ⓘ theorem in theoretical physics ⓘ
appliesTo	relativistic quantum field theories ⓘ theories with well-defined S-matrix ⓘ
assumption	Poincaré invariance ⓘ existence of a nontrivial analytic S-matrix ⓘ finitely many particle types below any given mass ⓘ mass gap between vacuum and first excited state ⓘ nontrivial scattering at almost all energies ⓘ positive energy spectrum bounded below ⓘ symmetry generators form a Lie algebra of bosonic operators ⓘ
clarifies	conditions under which spacetime and internal symmetries can be unified ⓘ
concerns	structure of symmetry groups in quantum field theory ⓘ unification of spacetime and internal symmetries ⓘ
conclusion	spacetime symmetries and internal symmetries cannot be nontrivially unified in an interacting quantum field theory with a nontrivial S-matrix ⓘ
doesNotApplyTo	conformal field theories without a standard S-matrix ⓘ theories with graded Lie algebras including fermionic generators ⓘ theories without a mass gap ⓘ two-dimensional integrable models with infinitely many conserved charges ⓘ
field	particle physics ⓘ quantum field theory ⓘ theoretical physics ⓘ
historicalImpact	motivated the search for symmetry extensions beyond ordinary Lie algebras ⓘ
implies	no nontrivial mixing of spacetime and internal symmetry generators in ordinary Lie algebras under its assumptions ⓘ
importance	foundational constraint on model building in high-energy physics ⓘ
inspired	Haag–Łopuszański–Sohnius theorem NERFINISHED ⓘ
mainStatement	under general assumptions the most general symmetry group of the S-matrix is a direct product of the Poincaré group and an internal symmetry group ⓘ
namedAfter	Jeffrey Mandula NERFINISHED ⓘ Sidney Coleman NERFINISHED ⓘ
publishedIn	Physical Review NERFINISHED ⓘ
relatedTo	Haag–Łopuszański–Sohnius theorem NERFINISHED ⓘ Poincaré group NERFINISHED ⓘ internal symmetry group ⓘ super-Poincaré algebra NERFINISHED ⓘ supersymmetry ⓘ
result	the Lie algebra of symmetries is a direct sum of the Poincaré algebra and an internal symmetry algebra ⓘ
shows	any additional bosonic symmetry generators must commute with Poincaré generators up to internal transformations ⓘ the full symmetry group is a direct product of spacetime and internal symmetry groups under its assumptions ⓘ
status	widely accepted ⓘ
typeOfSymmetryRestriction	no-go result for nontrivial bosonic unification of spacetime and internal symmetries ⓘ
usedIn	analysis of possible extensions of the Standard Model symmetries ⓘ arguments about limitations of grand unified theories ⓘ classification of possible symmetry groups of particle physics theories ⓘ
yearProved	1967 ⓘ

Referenced by (1)

Full triples — surface form annotated when it differs from this entity's canonical label.

Sidney Coleman → notableWork → Coleman–Mandula theorem ⓘ