Haag-Ruelle scattering theory
E284670
Haag-Ruelle scattering theory is a rigorous framework in quantum field theory that constructs and analyzes scattering states and S-matrix elements from local fields under mathematically precise conditions.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Haag-Ruelle scattering theory canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T2631174 — 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: Haag-Ruelle scattering theory Context triple: [LSZ reduction formula, relatedTo, Haag-Ruelle scattering theory]
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A.
Born approximation in scattering theory
The Born approximation in scattering theory is a perturbative method used in quantum mechanics to approximate scattering amplitudes by treating the interaction potential as a small perturbation to a free-particle wave.
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B.
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.
-
C.
Osterwalder–Schrader axioms
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.
-
D.
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.
-
E.
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.
- 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: Haag-Ruelle scattering theory Target entity description: Haag-Ruelle scattering theory is a rigorous framework in quantum field theory that constructs and analyzes scattering states and S-matrix elements from local fields under mathematically precise conditions.
-
A.
Born approximation in scattering theory
The Born approximation in scattering theory is a perturbative method used in quantum mechanics to approximate scattering amplitudes by treating the interaction potential as a small perturbation to a free-particle wave.
-
B.
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.
-
C.
Osterwalder–Schrader axioms
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.
-
D.
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.
-
E.
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.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
framework in quantum field theory
ⓘ
scattering theory ⓘ |
| addresses |
existence of scattering states in interacting quantum field theories
ⓘ
rigorous definition of particle states ⓘ |
| appliesTo |
massive quantum field theories
ⓘ
relativistic quantum field theories ⓘ |
| assumes | mass gap for massive particle scattering ⓘ |
| basedOn | local quantum field theory ⓘ |
| constructs |
asymptotic in-states
ⓘ
asymptotic out-states ⓘ multi-particle scattering states ⓘ |
| defines | S-matrix ⓘ |
| developedBy |
David Ruelle
ⓘ
Rudolf Haag ⓘ |
| developedIn | 1960s ⓘ |
| ensures |
Poincaré covariance of scattering states
ⓘ
cluster decomposition properties of scattering states ⓘ unitarity of the S-matrix under suitable assumptions ⓘ |
| field | quantum field theory ⓘ |
| hasApplication |
construction of particle interpretation in QFT
ⓘ
mathematical physics ⓘ rigorous study of interacting quantum fields ⓘ |
| hasMethod |
smearing of fields with test functions
ⓘ
strong limits as time goes to plus or minus infinity ⓘ time-dependent operators built from local fields ⓘ |
| hasPurpose |
construction of S-matrix elements
ⓘ
construction of scattering states ⓘ rigorous analysis of scattering in quantum field theory ⓘ |
| implies | asymptotic completeness under additional assumptions ⓘ |
| influenced | modern rigorous scattering theory in quantum field theory ⓘ |
| isRelatedTo |
Haag-Kastler axioms
ⓘ
Haag’s theorem ⓘ LSZ reduction formula ⓘ
surface form:
LSZ scattering theory
S-matrix theory ⓘ Wightman axioms ⓘ |
| requires |
existence of a unique vacuum state
ⓘ
locality of fields ⓘ positive energy condition ⓘ spectrum condition ⓘ stability of the vacuum ⓘ translation invariance ⓘ |
| usesConcept |
LSZ reduction formula
ⓘ
Wightman functions ⓘ
surface form:
Wightman fields
asymptotic limits of time-evolved fields ⓘ creation operators constructed from local fields ⓘ local fields ⓘ |
| usesFormalism | algebraic quantum field theory ⓘ |
How these facts were elicited
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Instruction
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Input
Subject: Haag-Ruelle scattering theory Description of subject: Haag-Ruelle scattering theory is a rigorous framework in quantum field theory that constructs and analyzes scattering states and S-matrix elements from local fields under mathematically precise conditions.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.