Quantum stochastic processes and noncommutative geometry
By: Kalyan B. Sinha, Debashish Goswami.
Contributors: Goswami, Debashish.
Edition: 1st ed.
Series: Cambridge tracts in mathematics
Publisher: Cambridge University Press
Published: 2007
Place of publication: Cambridge; New York
Language: eng
Number of pages: 290
ISBN-13: 9780521834506
Subjects: Stochastic processes; Quantum groups; Noncommutative differential geometry; Quantum theory
Description: The classical theory of stochastic processes has important applications arising from the need to describe irreversible evolutions in classical mechanics; analogously quantum stochastic processes can be used to model the dynamics of irreversible quantum systems. Noncommutative, id est quantum, geometry provides a framework in which quantum stochastic structures can be explored. This book is the first to describe how these two mathematical constructions are related. In particular, key ideas of semigroups and complete positivity are combined to yield quantum dynamical semigroups (QDS). Sinha and Goswami also develop a general theory of Evans-Hudson dilation for both bounded and unbounded coefficients. The unique features of the book, including the interaction of QDS and quantum stochastic calculus with noncommutative geometry and a thorough discussion of this calculus with unbounded coefficients, will make it of interest to graduate students and researchers in functional analysis, probability and mathematical physics.
Notes: Includes bibliographical references (p. 281-287) and index.
Table of contents: title: Introduction; title: Preliminaries; title: Quantum dynamical semigroups; title: Hilbert modules; title: Quantum stochastic calculus with bounded coefficients; title: Dilation of quantum dynamical semigroups with bounded generator; title: Quantum stochastic calculus with unbounded coefficients; title: Dilation of quantum dynamical semigroups with unbounded generator; title: Noncommutative geometry and quantum stochastic processes.