# Quantum Stochastic Calculus and Representations of Lie Superalgebras

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

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

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

- 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
- Buy this book on publisher's site