Dirac matrices
E118071
Dirac matrices are a set of matrices used in relativistic quantum mechanics to represent spin-½ particles and encode the algebra of the Dirac equation.
All labels observed (5)
| Label | Occurrences |
|---|---|
| Dirac basis | 1 |
| Dirac matrices canonical | 1 |
| Feynman slash notation | 1 |
| Majorana representation of the Dirac matrices | 1 |
| Weyl (chiral) basis | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1006224 — 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: Dirac matrices Context triple: [Dirac equation, uses, Dirac matrices]
-
A.
Gell-Mann matrices
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.
-
B.
Dirac equation
The Dirac equation is a fundamental relativistic wave equation in quantum mechanics that describes spin-½ particles such as electrons and predicts phenomena like antimatter.
-
C.
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.
-
D.
Feynman diagrams
Feynman diagrams are graphical representations used in quantum field theory to visualize and calculate particle interactions and processes.
-
E.
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.
- 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: Dirac matrices Target entity description: Dirac matrices are a set of matrices used in relativistic quantum mechanics to represent spin-½ particles and encode the algebra of the Dirac equation.
-
A.
Gell-Mann matrices
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.
-
B.
Dirac equation
The Dirac equation is a fundamental relativistic wave equation in quantum mechanics that describes spin-½ particles such as electrons and predicts phenomena like antimatter.
-
C.
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.
-
D.
Feynman diagrams
Feynman diagrams are graphical representations used in quantum field theory to visualize and calculate particle interactions and processes.
-
E.
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.
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical object
ⓘ
matrix family ⓘ representation of Clifford algebra ⓘ |
| actOn |
4-component spinors
ⓘ
Dirac spinors ⓘ |
| alsoKnownAs | gamma matrices ⓘ |
| anticommuteWith | γ^5 ⓘ |
| associatedWith |
Lorentz group
ⓘ
Minkowski space-time ⓘ
surface form:
Minkowski spacetime
|
| basisOf | space of 4×4 complex matrices ⓘ |
| define |
slashed four-vector γ^μ p_μ
ⓘ
γ^5 = i γ^0 γ^1 γ^2 γ^3 ⓘ |
| definedOver | complex numbers ⓘ |
| dimension | 4×4 ⓘ |
| encode |
algebraic structure of the Dirac equation
ⓘ
spinor structure of fermions ⓘ |
| haveRepresentation |
Dirac matrices
self-linksurface differs
ⓘ
surface form:
Dirac basis
Majorana basis ⓘ Dirac matrices self-linksurface differs ⓘ
surface form:
Weyl (chiral) basis
|
| include |
four gamma matrices γ^μ
ⓘ
identity matrix I ⓘ γ^5 ⓘ σ^{μν} = (i/2)[γ^μ, γ^ν] ⓘ |
| indexRange | μ = 0,1,2,3 ⓘ |
| introducedBy | Paul Dirac ⓘ |
| metricSignatureDependent | sign convention of η^{μν} ⓘ |
| numberOfIndependentMatrices | 16 ⓘ |
| obeyRelation |
{γ^μ, γ^ν} = 2 η^{μν} I
ⓘ
γ^μ γ^ν + γ^ν γ^μ = 2 η^{μν} I ⓘ |
| relatedTo | gamma matrices ⓘ |
| representationDependsOn | choice of basis ⓘ |
| representationOf |
Cl(1,3)
ⓘ
Clifford algebra of Minkowski metric ⓘ |
| satisfy |
Clifford algebra relations
ⓘ
anticommutation relations ⓘ |
| symbol | γ^μ ⓘ |
| usedIn |
Dirac equation
ⓘ
Dirac matrices self-linksurface differs ⓘ
surface form:
Feynman slash notation
quantum field theory ⓘ relativistic quantum mechanics ⓘ theory of spin-1/2 particles ⓘ |
| usedToConstruct |
Dirac Hamiltonian
ⓘ
Dirac operator ⓘ chirality operator γ^5 ⓘ |
| usedToDescribe |
fermionic fields
ⓘ
left-handed spinors ⓘ right-handed spinors ⓘ |
| usedToExpress |
Lorentz-covariant bilinears
ⓘ
spinor bilinears such as ψ̄γ^μψ ⓘ |
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: Dirac matrices Description of subject: Dirac matrices are a set of matrices used in relativistic quantum mechanics to represent spin-½ particles and encode the algebra of the Dirac equation.
Referenced by (5)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Dirac basis
this entity surface form:
Weyl (chiral) basis
this entity surface form:
Feynman slash notation
this entity surface form:
Majorana representation of the Dirac matrices