Noncommutative Mathematics for Quantum Systems - Adam Skalski

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Résumé :
Noncommutative mathematics is a significant new trend of mathematics. Initially motivated by the development of quantum physics, the idea of 'making theory noncommutative' has been extended to many areas of pure and applied mathematics. This book is divided into two parts. The 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 phenomena, never encountered in the classical setting. This book will be useful to students and researchers in noncommutative probability, mathematical physics and operator algebras.

Biographie:
Uwe Franz has been Professor at the University of Franche-Comt?, Besan?on, France, since 2005. He completed his PhD at Universit? Henri Poincar?-Nancy, France, in 1997. He was a Senior Fellow at the Alfried Krupp Wissenschaftskolleg Greifswald in 2014. He has authored one book, entitled Stochastic Processes and Operator Calculus on Quantum Groups (1999), edited four books on quantum probability, and written over fifty peer-reviewed research papers in the area of noncommutative mathematics. His areas of interest include noncommutative probability, quantum stochastic processes, quantum stochastic calculus and probability on quantum groups.

Sommaire:
Preface; Introduction; 1. Independence and L?vy processes in quantum probability; 2. Quantum dynamical systems from the point of view of noncommutative mathematics; Index.