Quantum Stochastic Calculus and Representations of Lie Superalgebras

1. Front Matter

   Pages I-VIII

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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. Representations of lie superalgebras in Z2-graded quantum stochastic calculus

   • Timothy M. W. Eyre

   Pages 33-50

6. The ungraded higher order Ito product formula

   • Timothy M. W. Eyre

   Pages 51-57

7. The Ito superalgebra

   • Timothy M. W. Eyre

   Pages 59-75

8. Some results in Z2-graded quantum stochastic calculus

   • Timothy M. W. Eyre

   Pages 77-99

9. Chaotic expansions

   • Timothy M. W. Eyre

   Pages 101-112

10. Extensions

    • Timothy M. W. Eyre

    Pages 113-132

11. Back Matter

    Pages 133-139

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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.

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

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