Quantum Stochastic Calculus and Representations of Lie Superalgebras [electronic resource] / by Timothy M. W. Eyre.
Material type: TextSeries: Lecture Notes in Mathematics ; 1692Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1998Description: VIII, 148 p. online resourceContent type:- text
- computer
- online resource
- 9783540683858
- 519.2 23
- QA273.A1-274.9
- QA274-274.9
Quantum stochastic calculus -- Z2-graded structures -- Representations of lie superalgebras in Z2-graded quantum stochastic calculus -- The ungraded higher order Ito product formula -- The Ito superalgebra -- Some results in Z2-graded quantum stochastic calculus -- Chaotic expansions -- Extensions.
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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