Skip to main content
SpringerLink
Log in
Birkhäuser

Symbol Correspondences for Spin Systems

  • Book
  • © 2014

Overview

Authors:
  1. Pedro de M. Rios

    1. Departamento de Matemática, Universidade de São Paulo, São Carlos, Brazil

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. Eldar Straume

    1. Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, Norway

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • 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: sn.pub/extras

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (10 chapters)

  1. Front Matter

    Pages i-ix
    Download chapter PDF

  2. Introduction

    • Pedro de M. Rios, Eldar Straume
    Pages 1-5

  3. Preliminaries

    • Pedro de M. Rios, Eldar Straume
    Pages 7-23

  4. Quantum Spin Systems and Their Operator Algebras

    • Pedro de M. Rios, Eldar Straume
    Pages 25-54

  5. The Poisson Algebra of the Classical Spin System

    • Pedro de M. Rios, Eldar Straume
    Pages 55-70

  6. Intermission

    • Pedro de M. Rios, Eldar Straume
    Pages 71-76

  7. Symbol Correspondences for a Spin-j System

    • Pedro de M. Rios, Eldar Straume
    Pages 77-104

  8. Multiplications of Symbols on the 2-Sphere

    • Pedro de M. Rios, Eldar Straume
    Pages 105-133

  9. Beginning Asymptotic Analysis of Twisted Products

    • Pedro de M. Rios, Eldar Straume
    Pages 135-157

  10. Conclusion

    • Pedro de M. Rios, Eldar Straume
    Pages 159-161

  11. Appendix: Further Proofs

    • Pedro de M. Rios, Eldar Straume
    Pages 163-191

  12. Back Matter

    Pages 193-200
    Download chapter PDF
Back to top

Keywords

About this book

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.

Reviews

From the book reviews:

“This book constitutes an interesting and highly useful monograph devoted to symbol correspondences, that will help the reader to better understand the existing relation between classical and quantum mechanics. For the particular case of physicists, this work will clarify the mathematical context and formalism that is not usually presented with such an amount of detail in other books on the subject. … This book is highly recommended to the specialist as well as to the non-specialist interested on spin systems.” (Rutwig Campoamor-Stursberg, zbMATH, Vol. 1305, 2015)

Authors and Affiliations

  • Departamento de Matemática, Universidade de São Paulo, São Carlos, Brazil

    Pedro de M. Rios

  • Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, Norway

    Eldar Straume

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation