04203nam 22007575 450 991029998240332120200630232723.03-319-08198-510.1007/978-3-319-08198-4(CKB)3710000000261951(EBL)1965354(OCoLC)896832292(SSID)ssj0001372809(PQKBManifestationID)11866426(PQKBTitleCode)TC0001372809(PQKBWorkID)11305158(PQKB)11142976(MiAaPQ)EBC1965354(DE-He213)978-3-319-08198-4(PPN)182093018(EXLCZ)99371000000026195120141010d2014 u| 0engur|n|---|||||txtccrSymbol Correspondences for Spin Systems /by Pedro de M. Rios, Eldar Straume1st ed. 2014.Cham :Springer International Publishing :Imprint: Birkhäuser,2014.1 online resource (204 p.)Description based upon print version of record.3-319-08197-7 Includes bibliographical references and index.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.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.Nonassociative ringsRings (Algebra)Quantum theoryTopological groupsLie groupsGeometry, DifferentialNon-associative Rings and Algebrashttps://scigraph.springernature.com/ontologies/product-market-codes/M11116Quantum Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/P19080Topological Groups, Lie Groupshttps://scigraph.springernature.com/ontologies/product-market-codes/M11132Differential Geometryhttps://scigraph.springernature.com/ontologies/product-market-codes/M21022Nonassociative rings.Rings (Algebra)Quantum theory.Topological groups.Lie groups.Geometry, Differential.Non-associative Rings and Algebras.Quantum Physics.Topological Groups, Lie Groups.Differential Geometry.510512.48512.55512482Rios Pedro de Mauthttp://id.loc.gov/vocabulary/relators/aut721279Straume Eldarauthttp://id.loc.gov/vocabulary/relators/autBOOK9910299982403321Symbol Correspondences for Spin Systems2529253UNINA