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While working on the mathematical physics of an interacting, relativistic, quantum field theory, Rudolf Haag developed an argument against the existence of the interaction picture, a result now commonly known as Haag’s theorem. Haag’s original proof relied on the specific form of then-common field theories, but subsequently generalized by a number of authors, notably Hall & Wightman, who concluded that no single, universal Hilbert space representation can describe both free and interacting fields. A generalization due to Reed & Simon shows that applies to free neutral scalar fields of different masses, which implies that the interaction picture is always inconsistent, even in the case of a free field.

Attributes	Values
rdf:type	yago:WikicatTheoremsInQuantumPhysics yago:Abstraction100002137 yago:Communication100033020 yago:Message106598915 yago:Proposition106750804 yago:Statement106722453 yago:Theorem106752293
rdfs:label	Haagsches Theorem (de) Haag's theorem (en) Teorema de Haag (pt)
rdfs:comment	Rudolf Haag formulierte ein Theorem, das heute allgemein als haagsches Theorem bekannt ist. Es besagt, dass das Wechselwirkungsbild einer relativistischen Quantenfeldtheorie (QFT) inkonsistent ist, d. h., nicht existiert.Haags Beweis von 1955 wurde anschließend mehrfach verallgemeinert, u. a. von Hall und Arthur Wightman, die zu dem Ergebnis gelangten, dass eine eindeutige, universelle Hilbertraum-Darstellung, die sowohl das freie als auch das wechselwirkende Feld beschreibt, nicht existiert.Reed und Simon zeigten 1975, dass ein analoges Theorem auch für neutrale, wechselwirkungsfreie Skalarfelder unterschiedlicher Massen existiert, woraus folgt, dass das Wechselwirkungsbild nicht einmal im Grenzfall einer vernachlässigbaren Wechselwirkung konsistent ist. (de) While working on the mathematical physics of an interacting, relativistic, quantum field theory, Rudolf Haag developed an argument against the existence of the interaction picture, a result now commonly known as Haag’s theorem. Haag’s original proof relied on the specific form of then-common field theories, but subsequently generalized by a number of authors, notably Hall & Wightman, who concluded that no single, universal Hilbert space representation can describe both free and interacting fields. A generalization due to Reed & Simon shows that applies to free neutral scalar fields of different masses, which implies that the interaction picture is always inconsistent, even in the case of a free field. (en)
dcterms:subject	Axiomatic quantum field theory Theorems in quantum mechanics
Wikipage page ID	796893 (xsd:integer)
Wikipage revision ID	1116595978 (xsd:integer)
Link from a Wikipage to another Wikipage	Canonical commutation relation Quantum electrodynamics Quantum field theory Quantum mechanics Rudolf Haag Scalar field Barry Simon David Ruelle Axiomatic quantum field theory Cyclic vector University of Pittsburgh Vacuum state Canonical commutation relations Eigenvalues and eigenvectors Standard Model Hamiltonian (quantum mechanics) Periodic boundary conditions Vacuum polarization Mathematical physics Michael C. Reed Theorems in quantum mechanics Irreducible representation Jet (particle physics) Local quantum field theory Number operator Isomorphism Ground state Hilbert space Arthur Wightman LSZ reduction formula Lawrence Sklar Wightman axioms CCR and CAR algebras Spacetime Special Relativity Free algebra Free field Interaction picture Self-adjoint operator Euclidean group Uncountable Haag–Ruelle scattering theory Mass (physics) Translation invariance Poincare invariance Representation of an algebra Wightman function Unitarily inequivalent
Link from a Wikipage to an external page	http://d-scholarship.pitt.edu/8260/
sameAs	Haag's theorem Haag's theorem Haag's theorem Haag's theorem Haag's theorem Haag's theorem Haag's theorem
dbp:wikiPageUsesTemplate	dbt:Cite_thesis dbt:Main dbt:Math dbt:Quantum-stub dbt:Reflist dbt:Sfn dbt:Short_description dbt:Use_dmy_dates
has abstract	Rudolf Haag formulierte ein Theorem, das heute allgemein als haagsches Theorem bekannt ist. Es besagt, dass das Wechselwirkungsbild einer relativistischen Quantenfeldtheorie (QFT) inkonsistent ist, d. h., nicht existiert.Haags Beweis von 1955 wurde anschließend mehrfach verallgemeinert, u. a. von Hall und Arthur Wightman, die zu dem Ergebnis gelangten, dass eine eindeutige, universelle Hilbertraum-Darstellung, die sowohl das freie als auch das wechselwirkende Feld beschreibt, nicht existiert.Reed und Simon zeigten 1975, dass ein analoges Theorem auch für neutrale, wechselwirkungsfreie Skalarfelder unterschiedlicher Massen existiert, woraus folgt, dass das Wechselwirkungsbild nicht einmal im Grenzfall einer vernachlässigbaren Wechselwirkung konsistent ist. (de) While working on the mathematical physics of an interacting, relativistic, quantum field theory, Rudolf Haag developed an argument against the existence of the interaction picture, a result now commonly known as Haag’s theorem. Haag’s original proof relied on the specific form of then-common field theories, but subsequently generalized by a number of authors, notably Hall & Wightman, who concluded that no single, universal Hilbert space representation can describe both free and interacting fields. A generalization due to Reed & Simon shows that applies to free neutral scalar fields of different masses, which implies that the interaction picture is always inconsistent, even in the case of a free field. (en)
prov:wasDerivedFrom	wikipedia-en:Haag's_theorem?oldid=1116595978&ns=0
page length (characters) of wiki page	14106 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Haag's_theorem
is Link from a Wikipage to another Wikipage of	Quantum field theory Rudolf Haag Index of physics articles (H) Mathematical formulation of quantum mechanics S-matrix No-go theorem Dynamical pictures Haag Wightman axioms Haag theorem Interaction picture List of theorems
is Wikipage redirect of	Haag theorem
is Wikipage disambiguates of	Haag
is known for of	Rudolf Haag

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