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Symbol Correspondences for Spin Systems

  • Pedro de M. Rios
  • Eldar Straume

Table of contents

  1. Front Matter
    Pages i-ix
  2. Pedro de M. Rios, Eldar Straume
    Pages 1-5
  3. Pedro de M. Rios, Eldar Straume
    Pages 7-23
  4. Pedro de M. Rios, Eldar Straume
    Pages 25-54
  5. Pedro de M. Rios, Eldar Straume
    Pages 55-70
  6. Pedro de M. Rios, Eldar Straume
    Pages 71-76
  7. Pedro de M. Rios, Eldar Straume
    Pages 77-104
  8. Pedro de M. Rios, Eldar Straume
    Pages 105-133
  9. Pedro de M. Rios, Eldar Straume
    Pages 135-157
  10. Pedro de M. Rios, Eldar Straume
    Pages 159-161
  11. Pedro de M. Rios, Eldar Straume
    Pages 163-191
  12. Back Matter
    Pages 193-200

About this book

Introduction

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.

Keywords

Poisson algebra on the two sphere SU(2)-invariant quantum systems dequantization quantum-classical symbol correspondences semiclassical asymptotic limit twisted products

Authors and affiliations

  • Pedro de M. Rios
    • 1
  • Eldar Straume
    • 2
  1. 1.Departamento de MatemáticaUniversidade de São PauloSão CarlosBrazil
  2. 2.Department of Mathematical SciencesNorwegian University of Science and TechnologyTrondheimNorway

Bibliographic information