spin–statistics theorem
E166678
The spin–statistics theorem is a fundamental result in quantum field theory that links a particle’s intrinsic spin to the type of quantum statistics it obeys, explaining why fermions obey the Pauli exclusion principle while bosons do not.
All labels observed (2)
| Label | Occurrences |
|---|---|
| spin–statistics theorem canonical | 2 |
| Spin–statistics theorem | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1462673 — 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: spin–statistics theorem Context triple: [Pauli exclusion principle, relatedTo, spin–statistics theorem]
-
A.
Bose–Einstein statistics
Bose–Einstein statistics is a quantum statistical framework that describes the distribution and collective behavior of indistinguishable bosons, underpinning phenomena such as Bose–Einstein condensation.
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B.
Wick’s theorem
Wick’s theorem is a fundamental result in quantum field theory that expresses time-ordered products of field operators as sums of normal-ordered products with all possible contractions, forming the basis for deriving Feynman rules and diagrammatic expansions.
-
C.
Fermi–Dirac statistics
Fermi–Dirac statistics is the quantum statistical framework that describes the distribution and behavior of indistinguishable fermions, such as electrons, which obey the Pauli exclusion principle.
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D.
Dirac field
The Dirac field is a quantum field describing spin-½ fermions, such as electrons and quarks, incorporating both special relativity and quantum mechanics.
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E.
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.
- 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: spin–statistics theorem Target entity description: The spin–statistics theorem is a fundamental result in quantum field theory that links a particle’s intrinsic spin to the type of quantum statistics it obeys, explaining why fermions obey the Pauli exclusion principle while bosons do not.
-
A.
Bose–Einstein statistics
Bose–Einstein statistics is a quantum statistical framework that describes the distribution and collective behavior of indistinguishable bosons, underpinning phenomena such as Bose–Einstein condensation.
-
B.
Wick’s theorem
Wick’s theorem is a fundamental result in quantum field theory that expresses time-ordered products of field operators as sums of normal-ordered products with all possible contractions, forming the basis for deriving Feynman rules and diagrammatic expansions.
-
C.
Fermi–Dirac statistics
Fermi–Dirac statistics is the quantum statistical framework that describes the distribution and behavior of indistinguishable fermions, such as electrons, which obey the Pauli exclusion principle.
-
D.
Dirac field
The Dirac field is a quantum field describing spin-½ fermions, such as electrons and quarks, incorporating both special relativity and quantum mechanics.
-
E.
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.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
result in quantum field theory
ⓘ
theorem ⓘ |
| appliesTo |
elementary particles
ⓘ
quantized fields ⓘ |
| assumes | relativistic quantum field theory ⓘ |
| connects |
commutation relations of fields
ⓘ
representation theory of the Lorentz group ⓘ |
| ensures |
causality in relativistic quantum field theory
ⓘ
positivity of probabilities ⓘ stability of the vacuum ⓘ |
| excludes | local relativistic fields with wrong spin–statistics connection ⓘ |
| explains | Pauli exclusion principle for fermions ⓘ |
| field | quantum field theory ⓘ |
| hasAlternativeFormulation |
Wightman axioms
ⓘ
surface form:
Wightman axioms framework
algebraic quantum field theory ⓘ |
| hasConsequence |
Bose–Einstein condensate
ⓘ
surface form:
Bose–Einstein condensation
properties of degenerate Fermi gases ⓘ stability of ordinary matter ⓘ structure of the periodic table ⓘ |
| implies |
bosonic wavefunctions are symmetric under particle exchange
ⓘ
bosons have integer spin ⓘ fermionic wavefunctions are antisymmetric under particle exchange ⓘ fermions have half-integer spin ⓘ half-integer-spin fields must anticommute at spacelike separation ⓘ integer-spin fields must commute at spacelike separation ⓘ no Pauli exclusion principle for bosons ⓘ |
| isAbout |
intrinsic angular momentum of particles
ⓘ
symmetry properties of many-particle wavefunctions ⓘ |
| isConsidered | fundamental principle of quantum field theory ⓘ |
| isRelatedTo |
Bose–Einstein statistics
ⓘ
CPT theorem ⓘ Fermi–Dirac statistics ⓘ Representations of groups ⓘ
surface form:
Lorentz group representations
Pauli exclusion principle ⓘ quantum commutation relations ⓘ |
| isUsedIn |
condensed matter physics
ⓘ
many-body quantum theory ⓘ standard model of particle physics ⓘ |
| relates |
particle spin
ⓘ
quantum statistics ⓘ |
| requires |
Lorentz invariance
ⓘ
locality ⓘ microcausality ⓘ positive energy spectrum ⓘ |
| states |
particles with half-integer spin obey Fermi–Dirac statistics
ⓘ
particles with integer spin obey Bose–Einstein statistics ⓘ |
| wasFirstProvedBy | Wolfgang Pauli ⓘ |
| yearOfFirstProof | 1940 ⓘ |
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: spin–statistics theorem Description of subject: The spin–statistics theorem is a fundamental result in quantum field theory that links a particle’s intrinsic spin to the type of quantum statistics it obeys, explaining why fermions obey the Pauli exclusion principle while bosons do not.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.