Noncommutative Mathematics for Quantum Systems

Uwe Franz; Adam Skalski

doi:10.1017/CBO9781316562857

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.

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Noncommutative Mathematics for Quantum Systems

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Contents

Frontmatter
pp i-iv

Dedication
pp v-vi

Contents
pp vii-x

Preface
pp xi-xii

Miscellaneous Frontmatter
pp xiii-xiii

Frontispiece
pp xiv-xiv

Introduction
pp xv-xviii

1 - Independence and Lévy Processes in Quantum Probability
pp 1-120

2 - Quantum Dynamical Systems from the Point of View of Noncommutative Mathematics
pp 121-172

References
pp 173-176

Index
pp 177-180

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