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  • © 1998

Quantum Stochastic Calculus and Representations of Lie Superalgebras

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

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Table of contents (9 chapters)

  1. Front Matter

    Pages I-VIII
  2. Introduction

    • Timothy M. W. Eyre
    Pages 1-6
  3. Quantum stochastic calculus

    • Timothy M. W. Eyre
    Pages 7-21
  4. Z2-graded structures

    • Timothy M. W. Eyre
    Pages 23-31
  5. The ungraded higher order Ito product formula

    • Timothy M. W. Eyre
    Pages 51-57
  6. The Ito superalgebra

    • Timothy M. W. Eyre
    Pages 59-75
  7. Chaotic expansions

    • Timothy M. W. Eyre
    Pages 101-112
  8. Extensions

    • Timothy M. W. Eyre
    Pages 113-132
  9. Back Matter

    Pages 133-139

About this book

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

  • Book Title: Quantum Stochastic Calculus and Representations of Lie Superalgebras

  • Authors: Timothy M. W. Eyre

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0096850

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1998

  • Softcover ISBN: 978-3-540-64897-0Published: 17 September 1998

  • eBook ISBN: 978-3-540-68385-8Published: 14 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VIII, 148

  • Topics: Probability Theory, Spintronics, Quantum Physics, Topological Groups and Lie Groups

Buying options

eBook USD 29.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 39.95
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions