Quantum Stochastic Calculus and Representations of Lie Superalgebras

Timothy M. W. Eyre (auth.)3540648976, 9783540648970

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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Table of contents :
Introduction….Pages 1-6
Quantum stochastic calculus….Pages 7-21
Z 2 -graded structures….Pages 23-31
Representations of lie superalgebras in Z 2 -graded quantum stochastic calculus….Pages 33-50
The ungraded higher order Ito product formula….Pages 51-57
The Ito superalgebra….Pages 59-75
Some results in Z 2 -graded quantum stochastic calculus….Pages 77-99
Chaotic expansions….Pages 101-112
Extensions….Pages 113-132