Kubo–Martin–Schwinger condition
E590893
criterion in quantum field theory
criterion in quantum statistical mechanics
equilibrium condition
mathematical condition in physics
The Kubo–Martin–Schwinger condition is a fundamental criterion in quantum statistical mechanics and quantum field theory that characterizes thermal equilibrium states through specific analyticity and periodicity properties of correlation functions.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Kubo–Martin–Schwinger condition canonical | 2 |
| Kubo–Martin–Schwinger equilibrium condition | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T6397129 — 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: Kubo–Martin–Schwinger condition Context triple: [Unruh effect, usesConcept, Kubo–Martin–Schwinger condition]
-
A.
Tomonaga–Schwinger equation
The Tomonaga–Schwinger equation is a relativistic generalization of the Schrödinger equation that formulates quantum field evolution on arbitrary spacelike hypersurfaces, forming a key part of covariant quantum field theory.
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B.
Bogoliubov–Parasyuk theorem
The Bogoliubov–Parasyuk theorem is a fundamental result in quantum field theory that rigorously establishes a systematic procedure for renormalizing divergent Feynman diagrams.
-
C.
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.
-
D.
Kramers–Kronig relations
The Kramers–Kronig relations are fundamental mathematical formulas in physics that connect the real and imaginary parts of a complex response function, expressing how causality constrains the frequency-dependent behavior of physical systems.
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E.
Ward–Takahashi identities
The Ward–Takahashi identities are fundamental relations in quantum field theory that express the consequences of gauge or global symmetries for Green’s functions and ensure the consistency of renormalization with these symmetries.
- 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: Kubo–Martin–Schwinger condition Target entity description: The Kubo–Martin–Schwinger condition is a fundamental criterion in quantum statistical mechanics and quantum field theory that characterizes thermal equilibrium states through specific analyticity and periodicity properties of correlation functions.
-
A.
Tomonaga–Schwinger equation
The Tomonaga–Schwinger equation is a relativistic generalization of the Schrödinger equation that formulates quantum field evolution on arbitrary spacelike hypersurfaces, forming a key part of covariant quantum field theory.
-
B.
Bogoliubov–Parasyuk theorem
The Bogoliubov–Parasyuk theorem is a fundamental result in quantum field theory that rigorously establishes a systematic procedure for renormalizing divergent Feynman diagrams.
-
C.
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.
-
D.
Kramers–Kronig relations
The Kramers–Kronig relations are fundamental mathematical formulas in physics that connect the real and imaginary parts of a complex response function, expressing how causality constrains the frequency-dependent behavior of physical systems.
-
E.
Ward–Takahashi identities
The Ward–Takahashi identities are fundamental relations in quantum field theory that express the consequences of gauge or global symmetries for Green’s functions and ensure the consistency of renormalization with these symmetries.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
criterion in quantum field theory
ⓘ
criterion in quantum statistical mechanics ⓘ equilibrium condition ⓘ mathematical condition in physics ⓘ |
| alsoKnownAs | KMS condition NERFINISHED ⓘ |
| appliesTo |
C*-algebraic dynamical systems
ⓘ
algebraic quantum field theory ⓘ quantum field theory ⓘ quantum statistical mechanics ⓘ |
| assumes | one-parameter automorphism group α_t ⓘ |
| characterizes | thermal equilibrium states ⓘ |
| connectedTo |
fluctuation–dissipation theorem
NERFINISHED
ⓘ
linear response theory ⓘ |
| definesPropertyOf |
Gibbs equilibrium states
ⓘ
states on C*-algebras ⓘ |
| expresses | β-periodicity of correlation functions in imaginary time ⓘ |
| formalizedBy | C*-algebra theory in the 1960s ⓘ |
| formalizedIn | operator algebra framework ⓘ |
| generalizes | classical detailed balance condition ⓘ |
| hasDomain | equilibrium quantum states ⓘ |
| hasRange | constraints on correlation functions ⓘ |
| historicallyIntroducedIn | 1950s ⓘ |
| implies |
detailed balance in quantum systems
ⓘ
time-translation invariance of the state ⓘ |
| involvesParameter | inverse temperature β ⓘ |
| mathematicallyExpressedAs | φ(A α_{iβ}(B)) = φ(BA) for all A,B in the algebra ⓘ |
| namedAfter |
Julian Schwinger
NERFINISHED
ⓘ
Paul C. Martin NERFINISHED ⓘ Ryogo Kubo NERFINISHED ⓘ |
| relatedTo |
Gibbs ensemble
NERFINISHED
ⓘ
Matsubara formalism NERFINISHED ⓘ Tomita–Takesaki modular theory NERFINISHED ⓘ canonical ensemble ⓘ imaginary-time formalism ⓘ modular automorphism group ⓘ thermal Green’s functions ⓘ |
| usedFor |
characterizing thermal states in infinite systems
ⓘ
constructing thermal quantum field theories ⓘ defining equilibrium without Hamiltonian spectrum assumptions ⓘ defining thermal correlation functions ⓘ |
| usedIn |
Hawking radiation analysis
ⓘ
Unruh effect analysis ⓘ algebraic approach to quantum statistical mechanics ⓘ thermal quantum field theory on curved spacetime ⓘ |
| usesConcept |
analyticity
ⓘ
correlation functions ⓘ periodicity in imaginary time ⓘ time-translation automorphism group ⓘ |
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: Kubo–Martin–Schwinger condition Description of subject: The Kubo–Martin–Schwinger condition is a fundamental criterion in quantum statistical mechanics and quantum field theory that characterizes thermal equilibrium states through specific analyticity and periodicity properties of correlation functions.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Kubo–Martin–Schwinger equilibrium condition