Quantum Stochastic Calculus and Representations of Lie Superalgebras

This book describes the forms of lie superalgebras yielded by a graded version of Hudson Parthasarathy quantum stochastic calculus. There is an introduction to quantum stochastic calculus and grading theory, extending readership to mathematicians and physicists with a basic knowledge of algebra and infinite dimensional Hilbert spaces. The development of an explicit formula for the chaotic expansion of a polynomial of quantum stochastic integrals is also looked into. This book aims to provide a self-contained exposition of what is known about Z2 graded quantum stochastic calculus and to provide a framework for future research into this fertile area.