Coleman–Mandula theorem
E573373
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.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Coleman–Mandula theorem canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T6155402 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Coleman–Mandula theorem Context triple: [Sidney Coleman, notableWork, Coleman–Mandula theorem]
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A.
Green–Schwarz mechanism
The Green–Schwarz mechanism is a key anomaly-cancellation process in string theory that ensures the mathematical consistency of certain superstring models by eliminating gauge and gravitational anomalies.
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B.
Gell-Mann–Low theorem
The Gell-Mann–Low theorem is a fundamental result in quantum field theory that rigorously connects interacting quantum fields to free fields via the adiabatic switching-on of interactions, underpinning the use of perturbation theory and the Dyson series.
-
C.
Ward–Takahashi identities
The Ward–Takahashi identities are fundamental relations in quantum field theory that express the consequences of gauge or global symmetries for Green’s functions and ensure the consistency of renormalization with these symmetries.
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D.
Kaluza–Klein theory
Kaluza–Klein theory is a higher-dimensional unification framework that extends general relativity by adding extra spatial dimensions to geometrically incorporate electromagnetism (and potentially other forces) alongside gravity.
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E.
Bogoliubov–Parasyuk theorem
The Bogoliubov–Parasyuk theorem is a fundamental result in quantum field theory that rigorously establishes a systematic procedure for renormalizing divergent Feynman diagrams.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Coleman–Mandula theorem Target entity description: 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.
-
A.
Green–Schwarz mechanism
The Green–Schwarz mechanism is a key anomaly-cancellation process in string theory that ensures the mathematical consistency of certain superstring models by eliminating gauge and gravitational anomalies.
-
B.
Gell-Mann–Low theorem
The Gell-Mann–Low theorem is a fundamental result in quantum field theory that rigorously connects interacting quantum fields to free fields via the adiabatic switching-on of interactions, underpinning the use of perturbation theory and the Dyson series.
-
C.
Ward–Takahashi identities
The Ward–Takahashi identities are fundamental relations in quantum field theory that express the consequences of gauge or global symmetries for Green’s functions and ensure the consistency of renormalization with these symmetries.
-
D.
Kaluza–Klein theory
Kaluza–Klein theory is a higher-dimensional unification framework that extends general relativity by adding extra spatial dimensions to geometrically incorporate electromagnetism (and potentially other forces) alongside gravity.
-
E.
Bogoliubov–Parasyuk theorem
The Bogoliubov–Parasyuk theorem is a fundamental result in quantum field theory that rigorously establishes a systematic procedure for renormalizing divergent Feynman diagrams.
- F. None of above. chosen
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 ⓘ |
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Input
Subject: Coleman–Mandula theorem Description of subject: 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.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.