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Noncommutative Mathematics for Quantum Systems

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Noncommutative Mathematics for Quantum Systems

Noncommutative Mathematics for Quantum Systems

Uwe Franz, Université de Franche-Comté
Adam Skalski, University of Warsaw, Poland
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9781316674406
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    Description

    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.

    • Provides an introduction to quantum probability
    • Presents an introduction to quantum dynamical systems
    • Discusses analogies with fundamental problems studied in classical dynamics

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    9781316674406
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    Contents

    Table of Contents

    • Preface
    • Introduction
    • 1. Independence and Lévy processes in quantum probability
    • 2. Quantum dynamical systems from the point of view of noncommutative mathematics
    • Index.
      • Show more
    Courses
    Resources
    Additional Information
    About the authors
      Authors
    • Uwe Franz , Université de Franche-Comté

      Uwe Franz has been Professor at the University of Franche-Comté, Besançon, France, since 2005. He completed his PhD at Université Henri Poincaré-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.

    • Adam Skalski , University of Warsaw, Poland

      Adam Skalski is an Associate Professor at the Mathematical Institute, Polish Academy of Sciences, University of Warsaw, Poland. He completed his PhD in Mathematics at the University of Nottingham in 2006. He has published a number of articles in the area of noncommutative mathematics. He has been awarded the Kuratowski Prize of the Polish Mathematical Society in 2008 and the Sierpiński Prize of the Polish Academy of Sciences in 2014. His areas of interest include topological quantum groups, noncommutative measure theory and quantum stochastic processes.

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