Gell-Mann matrices
E33749
Gell-Mann matrices are a set of eight 3×3 traceless Hermitian matrices that serve as the generators of the SU(3) Lie algebra in quantum chromodynamics and other areas of particle physics.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Gell-Mann matrices canonical | 2 |
| [λ_a, λ_b] = 2 i f_{abc} λ_c | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T259588 — 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: Gell-Mann matrices Context triple: [Murray Gell-Mann, knownFor, Gell-Mann matrices]
-
A.
S-matrix
The S-matrix (scattering matrix) is a fundamental construct in quantum field theory that encodes the probabilities for transitions between initial and final particle states in scattering processes.
-
B.
Lorentz group
The Lorentz group is the mathematical group of spacetime symmetries in special relativity, consisting of all rotations and boosts that preserve the Minkowski spacetime interval.
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C.
Feynman diagrams
Feynman diagrams are graphical representations used in quantum field theory to visualize and calculate particle interactions and processes.
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D.
SU(2)_L
SU(2)_L is the non-Abelian weak isospin gauge symmetry of the Standard Model that governs left-handed weak interactions.
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E.
Gaussian units
Gaussian units are a cgs-based system of electromagnetic units widely used in theoretical physics, especially in electrodynamics, for their mathematical simplicity and symmetry.
- 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: Gell-Mann matrices Target entity description: Gell-Mann matrices are a set of eight 3×3 traceless Hermitian matrices that serve as the generators of the SU(3) Lie algebra in quantum chromodynamics and other areas of particle physics.
-
A.
S-matrix
The S-matrix (scattering matrix) is a fundamental construct in quantum field theory that encodes the probabilities for transitions between initial and final particle states in scattering processes.
-
B.
Lorentz group
The Lorentz group is the mathematical group of spacetime symmetries in special relativity, consisting of all rotations and boosts that preserve the Minkowski spacetime interval.
-
C.
Feynman diagrams
Feynman diagrams are graphical representations used in quantum field theory to visualize and calculate particle interactions and processes.
-
D.
SU(2)_L
SU(2)_L is the non-Abelian weak isospin gauge symmetry of the Standard Model that governs left-handed weak interactions.
-
E.
Gaussian units
Gaussian units are a cgs-based system of electromagnetic units widely used in theoretical physics, especially in electrodynamics, for their mathematical simplicity and symmetry.
- F. None of above. chosen
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
Lie algebra generators
ⓘ
SU(3) generators ⓘ mathematical object ⓘ matrix basis set ⓘ |
| actOn |
color triplet of quarks
ⓘ
flavor triplet of quarks ⓘ three-component complex vectors ⓘ |
| are |
Hermitian
ⓘ
linearly independent ⓘ traceless ⓘ |
| basisOf | space of traceless Hermitian 3×3 matrices ⓘ |
| belongTo | fundamental representation of SU(3) ⓘ |
| cardinality | 8 ⓘ |
| componentType | complex entries ⓘ |
| dimension | 3×3 ⓘ |
| field |
particle physics
ⓘ
quantum chromodynamics ⓘ theoretical physics ⓘ |
| generalizationOf | Pauli matrices to SU(3) ⓘ |
| generate | SU(3) Lie algebra ⓘ |
| haveProperty |
off-diagonal elements for λ1, λ2, λ4, λ5, λ6, λ7
ⓘ
real diagonal elements for λ3 and λ8 ⓘ |
| indexRange | a = 1,…,8 ⓘ |
| matrixSize | 3 by 3 ⓘ |
| namedAfter | Murray Gell-Mann ⓘ |
| normalization | Tr(λ_a λ_b) = 2 δ_{ab} ⓘ |
| numberOfElements | 8 ⓘ |
| relatedTo | Pauli matrices ⓘ |
| satisfy |
[λ_a, λ_b] = 2 i f_{abc} λ_c
ⓘ
linked to:
Gell-Mann matrices
su(3) commutation relations ⓘ {λ_a, λ_b} = 4/3 δ_{ab} I + 2 d_{abc} λ_c ⓘ |
| span | Lie algebra su(3) ⓘ |
| symbol | λ_a ⓘ |
| usedFor |
classifying hadrons in the Eightfold Way
ⓘ
constructing SU(3) group elements via exponentiation ⓘ defining QCD gauge fields ⓘ writing QCD covariant derivative ⓘ |
| usedIn |
SU(3) Lie algebra
ⓘ
linked to:
SU(3)
color SU(3) symmetry ⓘ flavor SU(3) symmetry ⓘ gauge theories ⓘ quantum field theory ⓘ quark model ⓘ representation theory ⓘ |
| usedToRepresent |
color charge operators
ⓘ
flavor symmetry generators ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Gell-Mann matrices Description of subject: Gell-Mann matrices are a set of eight 3×3 traceless Hermitian matrices that serve as the generators of the SU(3) Lie algebra in quantum chromodynamics and other areas of particle physics.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Gell-Mann matrices