Stone–von Neumann theorem
E860124
The Stone–von Neumann theorem is a fundamental result in functional analysis and quantum mechanics that classifies all irreducible unitary representations of the canonical commutation relations as being unitarily equivalent.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Stone–von Neumann theorem canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T10389306 — 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: Stone–von Neumann theorem Context triple: [Weil representation, constructedVia, Stone–von Neumann theorem]
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A.
Gelfand–Naimark theorem
The Gelfand–Naimark theorem is a foundational result in functional analysis that characterizes C*-algebras as algebras of bounded operators on a Hilbert space (and, in the commutative case, as algebras of continuous functions on a locally compact Hausdorff space).
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B.
Stone’s theorem on one-parameter unitary groups
Stone’s theorem on one-parameter unitary groups is a fundamental result in functional analysis and quantum mechanics that characterizes strongly continuous one-parameter unitary groups as being generated by unique self-adjoint operators.
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C.
Peter–Weyl theorem
The Peter–Weyl theorem is a fundamental result in representation theory and harmonic analysis that decomposes square-integrable functions on a compact topological group into a direct sum of finite-dimensional irreducible unitary representations.
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D.
Wigner’s theorem on symmetry transformations
Wigner’s theorem on symmetry transformations is a fundamental result in quantum mechanics stating that any symmetry of transition probabilities is represented by either a unitary or antiunitary operator on the system’s Hilbert space.
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E.
Wigner–Eckart theorem
The Wigner–Eckart theorem is a fundamental result in quantum mechanics that factorizes matrix elements of tensor operators into a reduced matrix element and a purely geometric part given by Clebsch–Gordan coefficients, greatly simplifying angular momentum calculations.
- 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: Stone–von Neumann theorem Target entity description: The Stone–von Neumann theorem is a fundamental result in functional analysis and quantum mechanics that classifies all irreducible unitary representations of the canonical commutation relations as being unitarily equivalent.
-
A.
Gelfand–Naimark theorem
The Gelfand–Naimark theorem is a foundational result in functional analysis that characterizes C*-algebras as algebras of bounded operators on a Hilbert space (and, in the commutative case, as algebras of continuous functions on a locally compact Hausdorff space).
-
B.
Stone’s theorem on one-parameter unitary groups
Stone’s theorem on one-parameter unitary groups is a fundamental result in functional analysis and quantum mechanics that characterizes strongly continuous one-parameter unitary groups as being generated by unique self-adjoint operators.
-
C.
Peter–Weyl theorem
The Peter–Weyl theorem is a fundamental result in representation theory and harmonic analysis that decomposes square-integrable functions on a compact topological group into a direct sum of finite-dimensional irreducible unitary representations.
-
D.
Wigner’s theorem on symmetry transformations
Wigner’s theorem on symmetry transformations is a fundamental result in quantum mechanics stating that any symmetry of transition probabilities is represented by either a unitary or antiunitary operator on the system’s Hilbert space.
-
E.
Wigner–Eckart theorem
The Wigner–Eckart theorem is a fundamental result in quantum mechanics that factorizes matrix elements of tensor operators into a reduced matrix element and a purely geometric part given by Clebsch–Gordan coefficients, greatly simplifying angular momentum calculations.
- F. None of above. chosen
Statements (45)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical theorem
ⓘ
theorem in mathematical physics ⓘ theorem in representation theory ⓘ |
| appliesInContext | finite number of degrees of freedom ⓘ |
| appliesTo |
Weyl form of the canonical commutation relations
ⓘ
canonical commutation relations ⓘ irreducible unitary representations ⓘ |
| asserts |
all irreducible unitary representations of the canonical commutation relations are unitarily equivalent
ⓘ
there is essentially a unique irreducible unitary representation of the canonical commutation relations up to unitary equivalence ⓘ |
| characterizes | irreducible unitary representations of the canonical commutation relations ⓘ |
| concerns |
Heisenberg commutation relations
NERFINISHED
ⓘ
position and momentum operators ⓘ self-adjoint operators satisfying canonical commutation relations ⓘ |
| doesNotExtendTo | quantum field theory with infinitely many degrees of freedom ⓘ |
| field |
functional analysis
ⓘ
mathematical physics ⓘ operator algebras ⓘ quantum mechanics ⓘ representation theory ⓘ |
| formalizes | equivalence of all irreducible regular representations of the Weyl relations ⓘ |
| guarantees | uniqueness of the canonical quantization of finite-dimensional symplectic vector spaces ⓘ |
| hasConsequence |
equivalence of different realizations of the same quantum system
ⓘ
uniqueness of quantization for finite-dimensional canonical systems ⓘ |
| hasVersion | Weyl–Stone–von Neumann theorem NERFINISHED ⓘ |
| historicalPeriod | 20th century ⓘ |
| implies | uniqueness of the Schrödinger representation up to unitary equivalence ⓘ |
| namedAfter |
John von Neumann
NERFINISHED
ⓘ
Marshall H. Stone NERFINISHED ⓘ |
| relatedTo |
C*-algebras
ⓘ
CCR algebra NERFINISHED ⓘ Fock space representations ⓘ Heisenberg uncertainty principle NERFINISHED ⓘ Weyl quantization NERFINISHED ⓘ von Neumann algebras NERFINISHED ⓘ |
| requires |
irreducibility of the representation
ⓘ
regularity conditions on the representation ⓘ separability of the Hilbert space ⓘ |
| subjectOf |
Heisenberg group
NERFINISHED
ⓘ
Weyl relations NERFINISHED ⓘ canonical commutation relations ⓘ |
| usedIn |
classification of representations of the Heisenberg group
ⓘ
construction of the Schrödinger representation ⓘ mathematical foundations of quantum mechanics ⓘ |
| uses |
Weyl form of the canonical commutation relations
ⓘ
strong continuity of one-parameter unitary groups ⓘ |
How these facts were elicited
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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: Stone–von Neumann theorem Description of subject: The Stone–von Neumann theorem is a fundamental result in functional analysis and quantum mechanics that classifies all irreducible unitary representations of the canonical commutation relations as being unitarily equivalent.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.