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  3. Noncommutative Mathematics for Quantum Systems
  • Cited by 2
Publisher:
Cambridge University Press
Online publication date:
December 2015
Print publication year:
2016
Online ISBN:
9781316562857
DOI:
https://doi.org/10.1017/CBO9781316562857
Subjects:
Mathematics, Electronic, Optoelectronic Devices, and Nanotechnology, Abstract Analysis, Fluid Dynamics and Solid Mechanics, Discrete Mathematics Information Theory and Coding
Series:
Cambridge IISc Series
Information

Book 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.

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