Symbol Correspondences for Spin Systems

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Sprache: Englisch

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Beschreibung

In mathematical physics, the correspondence between quantum and classical mechanics is a central topic, which this book explores in more detail in the particular context of spin systems, that is, SU(2)-symmetric mechanical systems. A detailed presentation of quantum spin-j systems, with emphasis on the SO(3)-invariant decomposition of their operator algebras, is first followed by an introduction to the Poisson algebra of the classical spin system and then by a similarly detailed examination of its SO(3)-invariant decomposition. The book next proceeds with a detailed and systematic study of general quantum-classical symbol correspondences for spin-j systems and their induced twisted products of functions on the 2-sphere. This original systematic presentation culminates with the study of twisted products in the asymptotic limit of high spin numbers. In the context of spin systems it shows how classical mechanics may or may not emerge as an asymptotic limit of quantum mechanics. The book will be a valuable guide for researchers in this field and its self-contained approach also makes it a helpful resource for graduate students in mathematics and physics.

Zusammenfassung

Presents the SO(3)-invariant decomposition of the operator algebra of spin systems and of the Poisson algebra on the two sphere

Provides a full classification and detailed systematic presentation of symbol correspondences for spin systems and of general twisted products of symbols on the two sphere

Studies the high spin number asymptotic limit of symbol correspondence sequences and twisted products

Includes supplementary material: [...]

Inhaltsverzeichnis

Preface.- 1 Introduction.- 2 Preliminaries.- 3 Quantum Spin Systems and Their Operator Algebras.- 4 The Poisson Algebra of the Classical Spin System.- 5 Intermission.- 6 Symbol Correspondences for a Spin-j System.- 7 Multiplications of Symbols on the 2-Sphere.- 8 Beginning Asymptotic Analysis of Twisted Products.- 9 Conclusion.- Appendix.- Bibliography.- Index.

Details

Erscheinungsjahr:	2014
Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Inhalt:	ix 200 S.
ISBN-13:	9783319081977
ISBN-10:	3319081977
Sprache:	Englisch
Herstellernummer:	86359882
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Straume, Eldar Rios, Pedro de M.
Hersteller:	Springer International Publishing Springer International Publishing AG
Maße:	241 x 160 x 18 mm
Von/Mit:	Eldar Straume (u. a.)
Erscheinungsdatum:	27.10.2014
Gewicht:	0,489 kg

Artikel-ID: 105214603