Noncommutative Mathematics for Quantum Systems

Authors: Uwe Franz, University of Franche-Comté, Besançon, France; Adam Sklaski, Institute of Mathematics, Polish Academy of Sciences, Poland

Noncommutaitve mathematics is a significant new trend of mathematics in the twentieth century. This book is divided into two parts: first part provides an introduction to quantum probability, focusing on the notion of independence in quantum probability and on the theory of quantum stochastic processes with independent and stationary increments. The second part provides an introduction to quantum dynamical systems, discussing analogies with fundamental problems studied in classical dynamics. The desire to build an extension of the classical theory provides new, original ways to understand well-known ‘commutative’ results. On the other hand, the richness of the quantum mathematical world presents completely novel phenomenon, never encountered in the classical setting. This book will be useful to students and researchers in noncommutative probability, mathematical physics and operator algebras.

ISBN 978-1-107-14805-5 | First published in 2016 Co-publisher: Cambridge University Press