Operator Algebras in Dynamical Systems
Operator Algebras in Dynamical Systems by Shōichirō Sakai, published by Cambridge University Press on February 4, 2008, is a reissue edition comprising 232 pages. This book addresses the theory of unbounded derivations in C*-algebras, a field influenced by inquiries in quantum physics and statistical mechanics, where the author has made significant contributions. The work aims to advance the understanding of quantum statistical mechanics within the framework of C*-theory, focusing on the formulation of the absence theorem of phase transitions in a comprehensive manner.
Readers will find an in-depth exploration of topics related to quantum statistical mechanics and differentiations on manifolds. The author presents a global construction of derivations applicable to a broad class of interacting models for the first time, alongside a novel axiomatic approach to the construction of time evolutions and KMS states. This edition serves as a resource for those interested in the mathematical foundations of these concepts, particularly within the realms of mathematics, mathematical analysis, and calculus.
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This book is concerned with the theory of unbounded derivations in C*-algebras, a subject whose study was motivated by questions in quantum physics and statistical mechanics, and to which the author has made considerable contributions. This is an active area of research, and one of the most ambitious aims of the theory is to develop quantum statistical mechanics within the framework of C*-theory. The presentation concentrates on topics involving quantum statistical mechanics and differentiations on manifolds. One of the goals is to formulate the absence theorem of phase transitions in its most general form within the C* setting. For the first time, the author globally constructs, within that setting, derivations for a fairly wide class of interacting models, and presents a new axiomatic treatment of the construction of time evolutions and KMS states.
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