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Noncommutative Dynamics and E-Semigroups

  • William Arveson

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages i-x
  2. Dynamical Origins

    1. William Arveson
      Pages 1-15
  3. Index and Perturbation Theory

    1. Front Matter
      Pages 17-17
    2. William Arveson
      Pages 18-65
    3. William Arveson
      Pages 66-100
    4. William Arveson
      Pages 101-159
  4. Classification: Type I Cases

    1. Front Matter
      Pages 161-161
    2. William Arveson
      Pages 162-198
    3. William Arveson
      Pages 199-234
  5. Noncommutative Laplacians

    1. Front Matter
      Pages 235-235
    2. William Arveson
      Pages 236-253
    3. William Arveson
      Pages 254-303
    4. William Arveson
      Pages 304-323
    5. William Arveson
      Pages 324-354
  6. Causality and Dynamics

    1. Front Matter
      Pages 355-355
    2. William Arveson
      Pages 356-373
    3. William Arveson
      Pages 374-387
  7. Type III Examples

    1. Front Matter
      Pages 389-389
    2. William Arveson
      Pages 390-411
    3. William Arveson
      Pages 412-426
  8. Back Matter
    Pages 427-434

About this book

Introduction

 The term Noncommutative Dynamics can be interpreted in several ways. It is used in this book to refer to a set of phenomena associated with the dynamics of quantum systems of the simplest kind that involve rigorous mathematical structures associated with infinitely many degrees of freedom. The dynamics of such a system is represented by a one-parameter group of automorphisms of a noncommutative algebra of observables, and the author focuses primarily on the most concrete case in which that algebra consists of all bounded operators on a Hilbert space.

This subject overlaps with several mathematical areas of current interest, including quantum field theory, the dynamics of open quantum systems, noncommutative geometry, and both classical and noncommutative probability theory. This is the first book to give a systematic presentation of progress during the past fifteen years on the classification of E-semigroups up to cocycle conjugacy. There are many new results that cannot be found in the existing literature, as well as significant reformulations and simplifications of the theory as it exists today.

William Arveson is Professor of Mathematics at the University of California, Berkeley. He has published two previous books with Springer-Verlag, An Invitation to C*-algebras (1976) and A Short Course on Spectral Theory (2001).

Keywords

C*-algebra Hilbert space Mathematica algebra automorphism commutative algebra field index theory perturbation perturbation theory semigroup spectral theory

Authors and affiliations

  • William Arveson
    • 1
  1. 1.Department of MathematicsUniversity of California at BerkeleyBerkeleyUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-387-21524-2
  • Copyright Information Springer-Verlag New York 2003
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-1803-1
  • Online ISBN 978-0-387-21524-2
  • Series Print ISSN 1439-7382
  • Buy this book on publisher's site