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Inequivalent Representations of Canonical Commutation and Anti-Commutation Relations
Representation-theoretical Viewpoint for Quantum Phenomena
Buch von Asao Arai
Sprache: Englisch

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Beschreibung
Canonical commutation relations (CCR) and canonical anti-commutation relations (CAR) are basic principles in quantum physics including both quantum mechanics with finite degrees of freedom and quantum field theory. From a structural viewpoint, quantum physics can be primarily understood as Hilbert space representations of CCR or CAR. There are many interesting physical phenomena which can be more clearly understood from a representation¿theoretical viewpoint with CCR or CAR. This book provides an introduction to representation theories of CCR and CAR in view of quantum physics. Particular emphases are put on the importance of inequivalent representations of CCR or CAR, which may be related to characteristic physical phenomena. The topics presented include general theories of representations of CCR and CAR with finite and infinite degrees of freedom, the Aharonov¿Bohm effect, time operators, quantum field theories based on Fock spaces, Bogoliubov transformations, and relations of infinite renormalizations with inequivalent representations of CCR. This book can be used as a text for an advanced topics course in mathematical physics or mathematics.
Canonical commutation relations (CCR) and canonical anti-commutation relations (CAR) are basic principles in quantum physics including both quantum mechanics with finite degrees of freedom and quantum field theory. From a structural viewpoint, quantum physics can be primarily understood as Hilbert space representations of CCR or CAR. There are many interesting physical phenomena which can be more clearly understood from a representation¿theoretical viewpoint with CCR or CAR. This book provides an introduction to representation theories of CCR and CAR in view of quantum physics. Particular emphases are put on the importance of inequivalent representations of CCR or CAR, which may be related to characteristic physical phenomena. The topics presented include general theories of representations of CCR and CAR with finite and infinite degrees of freedom, the Aharonov¿Bohm effect, time operators, quantum field theories based on Fock spaces, Bogoliubov transformations, and relations of infinite renormalizations with inequivalent representations of CCR. This book can be used as a text for an advanced topics course in mathematical physics or mathematics.
Zusammenfassung

Presents a unified viewpoint for quantum physics, both in quantum mechanics and quantum field theory

Clarifies physical meanings of inequivalent representations of CCR or CAR

Gives representation-theoretical analyses to infinite renormalizations in some quantum field models

Includes representation-theoretical characterizations for fundamental quantities such as masses and charges

Contains mathematical descriptions in detail throughout the main text

Inhaltsverzeichnis
Mathematical Preliminaries.- Representations of Canonical Commutation Relations with Finite.- Aharonov-Bohm Effect and Inequivalent Representations of CCR.- Time Operators.- Representations of Canonical Anti-commutation Relations with Finite Degrees of Freedom.- Elements of the Theory of Boson Fock Spaces.- Elements of the Theory of Fermion Fock Spaces.- Representations of CCR with Infinite Degrees of Freedom.- Representations of CAR with Infinite Degrees of Freedom.- Physical Correspondences in Quantum Field Theory.
Details
Erscheinungsjahr: 2020
Fachbereich: Theoretische Physik
Genre: Physik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Mathematical Physics Studies
Inhalt: xix
493 S.
6 s/w Illustr.
493 p. 6 illus.
ISBN-13: 9789811521799
ISBN-10: 9811521794
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Arai, Asao
Auflage: 1st ed. 2020
Hersteller: Springer Singapore
Springer Nature Singapore
Mathematical Physics Studies
Maße: 241 x 160 x 34 mm
Von/Mit: Asao Arai
Erscheinungsdatum: 05.02.2020
Gewicht: 0,934 kg
Artikel-ID: 117798225
Zusammenfassung

Presents a unified viewpoint for quantum physics, both in quantum mechanics and quantum field theory

Clarifies physical meanings of inequivalent representations of CCR or CAR

Gives representation-theoretical analyses to infinite renormalizations in some quantum field models

Includes representation-theoretical characterizations for fundamental quantities such as masses and charges

Contains mathematical descriptions in detail throughout the main text

Inhaltsverzeichnis
Mathematical Preliminaries.- Representations of Canonical Commutation Relations with Finite.- Aharonov-Bohm Effect and Inequivalent Representations of CCR.- Time Operators.- Representations of Canonical Anti-commutation Relations with Finite Degrees of Freedom.- Elements of the Theory of Boson Fock Spaces.- Elements of the Theory of Fermion Fock Spaces.- Representations of CCR with Infinite Degrees of Freedom.- Representations of CAR with Infinite Degrees of Freedom.- Physical Correspondences in Quantum Field Theory.
Details
Erscheinungsjahr: 2020
Fachbereich: Theoretische Physik
Genre: Physik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Mathematical Physics Studies
Inhalt: xix
493 S.
6 s/w Illustr.
493 p. 6 illus.
ISBN-13: 9789811521799
ISBN-10: 9811521794
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Arai, Asao
Auflage: 1st ed. 2020
Hersteller: Springer Singapore
Springer Nature Singapore
Mathematical Physics Studies
Maße: 241 x 160 x 34 mm
Von/Mit: Asao Arai
Erscheinungsdatum: 05.02.2020
Gewicht: 0,934 kg
Artikel-ID: 117798225
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