Osterwalder–Schrader axioms
E59638
The Osterwalder–Schrader axioms are a set of mathematical conditions that characterize Euclidean quantum field theories in a way that allows them to be rigorously continued to physically meaningful relativistic quantum field theories.
All labels observed (4)
How this entity was disambiguated
This entity first appeared as the object of triple T478499 — 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: Osterwalder–Schrader axioms Context triple: [Euclidean quantum field theory, hasKeyConcept, Osterwalder–Schrader axioms]
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A.
Faddeev’s axioms
Faddeev’s axioms are a set of conditions characterizing Shannon entropy in information theory, providing an alternative but equivalent axiomatization to the Shannon–Khinchin framework.
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B.
Euclidean quantum field theory
Euclidean quantum field theory is a formulation of quantum field theory in imaginary (Euclidean) time that enables rigorous mathematical treatment and path-integral representations closely connected to statistical mechanics.
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C.
Mathematical Foundations of Quantum Mechanics
Mathematical Foundations of Quantum Mechanics is John von Neumann’s landmark 1932 treatise that rigorously formulates quantum theory using functional analysis and operator theory on Hilbert spaces.
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D.
Dyson’s proof of equivalence of Feynman and Schwinger–Tomonaga formulations of QED
Dyson’s proof of equivalence of Feynman and Schwinger–Tomonaga formulations of QED is a landmark theoretical result that rigorously demonstrated the mathematical consistency and mutual compatibility of different approaches to quantum electrodynamics.
-
E.
Feynman–Kac formula
The Feynman–Kac formula is a fundamental result connecting solutions of certain partial differential equations with expectations over stochastic processes, forming a bridge between quantum mechanics, probability theory, and mathematical finance.
- 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: Osterwalder–Schrader axioms Target entity description: The Osterwalder–Schrader axioms are a set of mathematical conditions that characterize Euclidean quantum field theories in a way that allows them to be rigorously continued to physically meaningful relativistic quantum field theories.
-
A.
Faddeev’s axioms
Faddeev’s axioms are a set of conditions characterizing Shannon entropy in information theory, providing an alternative but equivalent axiomatization to the Shannon–Khinchin framework.
-
B.
Euclidean quantum field theory
Euclidean quantum field theory is a formulation of quantum field theory in imaginary (Euclidean) time that enables rigorous mathematical treatment and path-integral representations closely connected to statistical mechanics.
-
C.
Mathematical Foundations of Quantum Mechanics
Mathematical Foundations of Quantum Mechanics is John von Neumann’s landmark 1932 treatise that rigorously formulates quantum theory using functional analysis and operator theory on Hilbert spaces.
-
D.
Dyson’s proof of equivalence of Feynman and Schwinger–Tomonaga formulations of QED
Dyson’s proof of equivalence of Feynman and Schwinger–Tomonaga formulations of QED is a landmark theoretical result that rigorously demonstrated the mathematical consistency and mutual compatibility of different approaches to quantum electrodynamics.
-
E.
Feynman–Kac formula
The Feynman–Kac formula is a fundamental result connecting solutions of certain partial differential equations with expectations over stochastic processes, forming a bridge between quantum mechanics, probability theory, and mathematical finance.
- F. None of above. chosen
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
axiomatic system
ⓘ
set of mathematical conditions ⓘ |
| allows | reconstruction of relativistic quantum field theories from Euclidean correlation functions ⓘ |
| appliesTo |
Euclidean quantum field theory
ⓘ
surface form:
Euclidean quantum field theories
|
| assumes |
Euclidean space
ⓘ
surface form:
Euclidean space-time
|
| basedOn |
Euclidean invariance
ⓘ
cluster properties ⓘ reflection positivity ⓘ regularity conditions ⓘ symmetry ⓘ |
| characterizes | which Euclidean field theories correspond to physical relativistic theories ⓘ |
| concerns |
Euclidean correlation functions
ⓘ
Schwinger functions ⓘ |
| context |
probability measures on spaces of distributions
ⓘ
rigorous quantum field theory ⓘ |
| field |
Euclidean quantum field theory
ⓘ
mathematical physics ⓘ quantum field theory ⓘ |
| formalism |
Euclidean quantum field theory
ⓘ
surface form:
Euclidean path integral
|
| guarantees |
locality of the reconstructed quantum fields
ⓘ
positivity of the inner product after reconstruction ⓘ spectrum condition for the Hamiltonian ⓘ |
| implies |
Osterwalder–Schrader axioms
self-linksurface differs
ⓘ
surface form:
Wightman axioms for the reconstructed Minkowski theory
existence of a Hilbert space of states ⓘ existence of a self-adjoint Hamiltonian ⓘ unitary representation of the Poincaré group after continuation ⓘ |
| includesCondition |
Euclidean invariance of Schwinger functions
ⓘ
cluster decomposition property ⓘ reflection positivity of Schwinger functions ⓘ regularity and growth bounds on Schwinger functions ⓘ symmetry of Schwinger functions under permutations of arguments ⓘ |
| introducedBy |
Konrad Osterwalder
ⓘ
Robert Schrader ⓘ |
| namedAfter |
Konrad Osterwalder
ⓘ
Robert Schrader ⓘ |
| publicationType | results published in mathematical physics papers ⓘ |
| purpose |
to allow analytic continuation from Euclidean to Minkowski space
ⓘ
to characterize Euclidean quantum field theories that correspond to relativistic quantum field theories ⓘ |
| relatedTo |
Minkowski space quantum field theory
ⓘ
Schwinger functions ⓘ Wightman axioms ⓘ analytic continuation ⓘ |
| requires | reflection with respect to a Euclidean time coordinate ⓘ |
| timePeriod | 1970s ⓘ |
| usedFor |
constructive quantum field theory
ⓘ
rigorous formulation of quantum field theory ⓘ |
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Input
Subject: Osterwalder–Schrader axioms Description of subject: The Osterwalder–Schrader axioms are a set of mathematical conditions that characterize Euclidean quantum field theories in a way that allows them to be rigorously continued to physically meaningful relativistic quantum field theories.
Referenced by (12)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Osterwalder–Schrader reconstruction theorem
this entity surface form:
Osterwalder–Schrader reconstruction theorem
this entity surface form:
Wightman axioms for the reconstructed Minkowski theory
this entity surface form:
Osterwalder–Schrader reconstruction via analytic continuation
this entity surface form:
Osterwalder–Schrader reconstruction theorem
this entity surface form:
Osterwalder–Schrader reconstruction theorem