Noncommutative Mathematics for Quantum Systems

This book provides an introduction to quantum probability, focusing on the notion of independence in quantum probability.

Uwe Franz (Author), Adam Skalski (Author)

9781107148055, Cambridge University Press

Hardback, published 7 January 2016

125 pages
23.5 x 15.8 x 1.5 cm, 0.4 kg

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.

Preface
Introduction
1. Independence and Lévy processes in quantum probability
2. Quantum dynamical systems from the point of view of noncommutative mathematics
Index.

Subject Areas: Mathematical physics [PHU], Quantum physics [quantum mechanics & quantum field theory PHQ], Physics [PH], Calculus & mathematical analysis [PBK], Algebra [PBF], Mathematics [PB]