Quantum Stochastic Calculus and Representations of Lie Superalgebras

  • Authors
  • Timothy M. W. Eyre

Part of the Lecture Notes in Mathematics book series (LNM, volume 1692)

Table of contents

  1. Front Matter
    Pages I-VIII
  2. Timothy M. W. Eyre
    Pages 1-6
  3. Timothy M. W. Eyre
    Pages 7-21
  4. Timothy M. W. Eyre
    Pages 23-31
  5. Timothy M. W. Eyre
    Pages 51-57
  6. Timothy M. W. Eyre
    Pages 59-75
  7. Timothy M. W. Eyre
    Pages 101-112
  8. Timothy M. W. Eyre
    Pages 113-132
  9. Back Matter
    Pages 133-139

About this book

Introduction

This book describes the representations of Lie superalgebras that are yielded by a graded version of Hudson-Parthasarathy quantum stochastic calculus. Quantum stochastic calculus and grading theory are given concise introductions, extending readership to mathematicians and physicists with a basic knowledge of algebra and infinite-dimensional Hilbert spaces. The develpment of an explicit formula for the chaotic expansion of a polynomial of quantum stochastic integrals is particularly interesting. The book aims to provide a self-contained exposition of what is known about Z_2-graded quantum stochastic calculus and to provide a framework for future research into this new and fertile area.

Keywords

Chaotic expansion Lie superalgebra Quantum probability Quantum stochastic calculus Stochastic calculus Universal enveloping algebra

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0096850
  • Copyright Information Springer-Verlag Berlin Heidelberg 1998
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-64897-0
  • Online ISBN 978-3-540-68385-8
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book