Pauli matrices
E179974
Pauli matrices are a set of three 2×2 complex Hermitian and unitary matrices that form a basis for the Lie algebra su(2) and are fundamental in describing spin-½ particles in quantum mechanics.
All labels observed (3)
| Label | Occurrences |
|---|---|
| Pauli matrices canonical | 5 |
| Pauli spin matrices | 2 |
| Pauli operators | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1580420 — 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: Pauli matrices Context triple: [Gell-Mann matrices, relatedTo, Pauli matrices]
-
A.
Dirac matrices
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.
-
B.
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.
-
C.
Dirac spinors
Dirac spinors are four-component mathematical objects in relativistic quantum mechanics that describe spin-½ particles, such as electrons, incorporating both their spin and particle–antiparticle degrees of freedom.
-
D.
Pauli equation
The Pauli equation is a non-relativistic quantum mechanical wave equation that extends the Schrödinger equation to include spin-½ particles interacting with electromagnetic fields.
-
E.
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.
- 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: Pauli matrices Target entity description: Pauli matrices are a set of three 2×2 complex Hermitian and unitary matrices that form a basis for the Lie algebra su(2) and are fundamental in describing spin-½ particles in quantum mechanics.
-
A.
Dirac matrices
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.
-
B.
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.
-
C.
Dirac spinors
Dirac spinors are four-component mathematical objects in relativistic quantum mechanics that describe spin-½ particles, such as electrons, incorporating both their spin and particle–antiparticle degrees of freedom.
-
D.
Pauli equation
The Pauli equation is a non-relativistic quantum mechanical wave equation that extends the Schrödinger equation to include spin-½ particles interacting with electromagnetic fields.
-
E.
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.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
basis of Lie algebra
ⓘ
mathematical object ⓘ matrix family ⓘ |
| alsoKnownAs |
Pauli matrices
ⓘ
surface form:
Pauli operators
Pauli matrices ⓘ
surface form:
Pauli spin matrices
|
| anticommutationRelation | {σ_i, σ_j} = 2 δ_ij I ⓘ |
| basisOf |
2×2 traceless Hermitian matrices
ⓘ
Lie algebras ⓘ
surface form:
Lie algebra of SU(2)
|
| belongsToGroup | Pauli group ⓘ |
| commutationRelation | [σ_i, σ_j] = 2 i ε_ijk σ_k ⓘ |
| component |
sigma_x
ⓘ
sigma_y ⓘ sigma_z ⓘ |
| determinantProperty | det(σ_i) = -1 ⓘ |
| eigenvalues |
+1
ⓘ
-1 ⓘ |
| entryType | complex numbers ⓘ |
| field |
linear algebra
ⓘ
mathematical physics ⓘ quantum mechanics ⓘ representation theory ⓘ |
| formsBasisFor |
Lie algebra su(2)
ⓘ
su(2) ⓘ |
| hasCardinality | 3 ⓘ |
| matrixSize |
2×2
ⓘ
two-by-two ⓘ |
| namedAfter | Wolfgang Pauli ⓘ |
| property |
Hermitian
ⓘ
unitary ⓘ |
| relatedConcept |
Poincaré sphere
ⓘ
surface form:
Bloch sphere
SO(3) ⓘ rotation group SU(2) ⓘ
surface form:
SU(2)
qubit ⓘ spin operator ⓘ |
| squareProperty | σ_i^2 = I ⓘ |
| traceProperty | Tr(σ_i) = 0 ⓘ |
| usedFor |
SU(2) representation
ⓘ
description of spin-1/2 particles ⓘ qubit operations ⓘ representation of angular momentum operators ⓘ spin operators in quantum mechanics ⓘ two-level quantum systems ⓘ |
| usedIn |
Dirac equation representation
ⓘ
Pauli equation ⓘ non-relativistic quantum mechanics ⓘ quantum computing ⓘ quantum information theory ⓘ spinor formalism ⓘ |
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: Pauli matrices Description of subject: Pauli matrices are a set of three 2×2 complex Hermitian and unitary matrices that form a basis for the Lie algebra su(2) and are fundamental in describing spin-½ particles in quantum mechanics.
Referenced by (8)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Pauli spin matrices
this entity surface form:
Pauli spin matrices
this entity surface form:
Pauli operators