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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Editorial Reviews
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"The theory for the normal derivations is developed very clearly in this important book, and the subject is one of the most central ones in the modern theory of operator algebras. It is written by one of the prime movers, and it is addressed to a wide audience. It should be a useful introduction to the subject." Palle E.T. Jørgensen, Mathematical Reviews
"...makes for pleasant browsing and really worthwhile reading....This volume is a gem!" Richard V. Kadison, Bulletin of the American Mathematical Society
"...makes for pleasant browsing and really worthwhile reading....This volume is a gem!" Richard V. Kadison, Bulletin of the American Mathematical Society
Book Description
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 a considerable contribution. This presentation concentrates on topics involving quantum statistical mechanics and differentiations on manifolds.
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Front Cover | Front Flap | Table of Contents | First Pages | Index | Back Flap | Back Cover | Surprise Me!
Inside This Book
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First Sentence:
In this chapter we shall state some fundamental facts used in this book. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
continuous quantum systems, time automorphism group, unbounded derivations, quantum lattice systems, connected locally euclidean space, locally normal state, absence theorem, mutually commuting family, closed derivations, classical lattice systems, physical ground state, tracial state, covariant representation, strongly continuous unitary representation, interacting models, uniform closure, bounded perturbations, full matrix algebra, weak operator topology, affirmative solution, weak closure, strong operator topology, finite range interaction, invariant state, lim exp Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proposition Let, Proof Let, Lemma Let, Proof Suppose, Definition Let, Proposition Suppose, Corollary Let, Problem Let, Problem Can, Theorem Suppose, Lemma Suppose, Let Aut, Proof Put, Proof Take New!
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Front Cover | Front Flap | Table of Contents | First Pages | Index | Back Flap | Back Cover | Surprise Me!
In this chapter we shall state some fundamental facts used in this book. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
continuous quantum systems, time automorphism group, unbounded derivations, quantum lattice systems, connected locally euclidean space, locally normal state, absence theorem, mutually commuting family, closed derivations, classical lattice systems, physical ground state, tracial state, covariant representation, strongly continuous unitary representation, interacting models, uniform closure, bounded perturbations, full matrix algebra, weak operator topology, affirmative solution, weak closure, strong operator topology, finite range interaction, invariant state, lim exp Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proposition Let, Proof Let, Lemma Let, Proof Suppose, Definition Let, Proposition Suppose, Corollary Let, Problem Let, Problem Can, Theorem Suppose, Lemma Suppose, Let Aut, Proof Put, Proof Take New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Front Flap | Table of Contents | First Pages | Index | Back Flap | Back Cover | Surprise Me!
Citations (learn more)
This book cites 11
books:
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30
books
cite this book:
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- Topological Transformation Groups by D. Montgomery in Back Matter
- Operator Algebras and Applications (Proceedings of Symposia in Pure Mathematics, vol. 38, pt. 1) by Richard V. Kadison in Back Matter
- Real and Complex Analysis (International Series in Pure and Applied Mathematics) by Walter Rudin in Back Matter
- Smooth Dynamical Systems (Advanced Series in Nonlinear Dynamics) by Michael Charles Irwin in Back Matter
- Analytic Function Theory, Volume I (AMS Chelsea Publishing) by Einar Hille in Back Matter
See all 11 books this book cites
- Skew Fields: Theory of General Division Rings (Encyclopedia of Mathematics and its Applications) by P. M. Cohn FRS in Front Matter
- Stopping Times and Directed Processes (Encyclopedia of Mathematics and its Applications) by G. A. Edgar in Front Matter
- Computation with Finitely Presented Groups (Encyclopedia of Mathematics and its Applications) by Charles C. Sims in Front Matter
- Convex Bodies: The Brunn-Minkowski Theory (Encyclopedia of Mathematics and its Applications) by Rolf Schneider in Front Matter
- Design Theory: Volume 2 (Encyclopedia of Mathematics and its Applications) by Thomas Beth in Front Matter
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