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Quantum Stochastic Calculus and Representations of Lie Superalgebras

  • Book
  • © 1998
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Overview

Authors:
  1. Timothy M. W. Eyre
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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
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  2. Introduction

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

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

    • Timothy M. W. Eyre
    Pages 23-31
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  5. Representations of lie superalgebras in Z2-graded quantum stochastic calculus

    • Timothy M. W. Eyre
    Pages 33-50
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  6. The ungraded higher order Ito product formula

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

    • Timothy M. W. Eyre
    Pages 59-75
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  8. Some results in Z2-graded quantum stochastic calculus

    • Timothy M. W. Eyre
    Pages 77-99
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  9. Chaotic expansions

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

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

    Pages 133-139
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Keywords

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.

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