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Cover: 9783662140789 | Translation Group and Particle Representations in Quantum Field Theory
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Translation Group and Particle Representations in Quantum Field Theory
Taschenbuch von Hans-Jürgen Borchers
Sprache: Englisch

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Beschreibung
At the time I learned quantum field theory it was considered a folk theo­ rem that it is easy to construct field theories fulfilling either the locality or the spectrum condition. The construction of an example for the latter case is particularly easy. Take for instance an irreducible representation of the Poincare group with positive energy, and as an algebra of observables all compact operators in that representation space. This algebra of observables is even an asymptotically Abelian algebra. Since it has only a single repre­ sentation - except for multiples of this one - it is hardly possible to replace locality in order to obtain a theory with a reasonable physical structure. This example shows that it is not sufficient to replace locality by asymptotic Abelian-ness. The construction of a theory fulfilling locality without a pos­ itive energy representation was first done by Doplicher, Regge, and Singer [DRS]. However, modern investigations on the locality ideal in the algebra oftest functions, started by Alcantara and Yngvason [AY], seem to indicate that this is a general feature; this means that most of the algebras of ob­ servables fulfilling the locality condition will not have representations that also fulfil the spectrum condition. This discussion shows that quantum field theory becomes a subject of interest only if both conditions are satisfied at the same time.
At the time I learned quantum field theory it was considered a folk theo­ rem that it is easy to construct field theories fulfilling either the locality or the spectrum condition. The construction of an example for the latter case is particularly easy. Take for instance an irreducible representation of the Poincare group with positive energy, and as an algebra of observables all compact operators in that representation space. This algebra of observables is even an asymptotically Abelian algebra. Since it has only a single repre­ sentation - except for multiples of this one - it is hardly possible to replace locality in order to obtain a theory with a reasonable physical structure. This example shows that it is not sufficient to replace locality by asymptotic Abelian-ness. The construction of a theory fulfilling locality without a pos­ itive energy representation was first done by Doplicher, Regge, and Singer [DRS]. However, modern investigations on the locality ideal in the algebra oftest functions, started by Alcantara and Yngvason [AY], seem to indicate that this is a general feature; this means that most of the algebras of ob­ servables fulfilling the locality condition will not have representations that also fulfil the spectrum condition. This discussion shows that quantum field theory becomes a subject of interest only if both conditions are satisfied at the same time.
Inhaltsverzeichnis
The Axioms of the Theory of Local Observables.- Translations and the Spectrum Condition.- The Opposite Edge of the Wedge Problem.- Locality Condition and the Spectrum of Translations.
Details
Erscheinungsjahr: 2014
Fachbereich: Theoretische Physik
Genre: Physik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 148
Reihe: Lecture Notes in Physics Monographs
Inhalt: vii
136 S.
9 s/w Illustr.
136 p. 9 illus.
ISBN-13: 9783662140789
ISBN-10: 3662140780
Sprache: Englisch
Herstellernummer: 86220850
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Borchers, Hans-Jürgen
Auflage: Softcover reprint of the original 1st ed. 1996
Hersteller: Springer Berlin
Springer Berlin Heidelberg
Lecture Notes in Physics Monographs
Maße: 235 x 155 x 9 mm
Von/Mit: Hans-Jürgen Borchers
Erscheinungsdatum: 18.04.2014
Gewicht: 0,236 kg
preigu-id: 105278647
Inhaltsverzeichnis
The Axioms of the Theory of Local Observables.- Translations and the Spectrum Condition.- The Opposite Edge of the Wedge Problem.- Locality Condition and the Spectrum of Translations.
Details
Erscheinungsjahr: 2014
Fachbereich: Theoretische Physik
Genre: Physik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 148
Reihe: Lecture Notes in Physics Monographs
Inhalt: vii
136 S.
9 s/w Illustr.
136 p. 9 illus.
ISBN-13: 9783662140789
ISBN-10: 3662140780
Sprache: Englisch
Herstellernummer: 86220850
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Borchers, Hans-Jürgen
Auflage: Softcover reprint of the original 1st ed. 1996
Hersteller: Springer Berlin
Springer Berlin Heidelberg
Lecture Notes in Physics Monographs
Maße: 235 x 155 x 9 mm
Von/Mit: Hans-Jürgen Borchers
Erscheinungsdatum: 18.04.2014
Gewicht: 0,236 kg
preigu-id: 105278647
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