UID:
almafu_9959240256002883
Format:
1 online resource (xi, 219 pages) :
,
digital, PDF file(s).
ISBN:
1-139-88464-6
,
0-511-95200-7
,
1-107-10285-5
,
1-107-09445-3
,
1-107-08823-2
,
0-511-66221-1
Series Statement:
Encyclopedia of mathematics and its applications ; v. 41
Content:
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 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 the C*-theory. The presentation, which is based on lectures given in Newcastle upon Tyne and Copenhagen, 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, he 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.
Note:
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
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Cover; Half-title; Title; Copyright; Contents; Preface; 1 Preliminaries; 1.1 Banach algebras, C*-algebras and W*-algebras; 1.2 Topologies on C*-algebras and W*-algebras; 1.3 Homomorphisms, *-isomorphisms and *-automorphisms; 1.4 Self-adjointness and positivity; 1.5 Positive linear functionals and states; 1.6 Commutative C*- and W*-algebras; 1.7 Concrete C*- and W*-algebras; 1.8 Representation theorems for C*- and W*-algebras; 1.9 Commutation theorem (von Neumann's double commutant theorem); 1.10 Kaplansky's density theorem (Bounded approximations); 1.11 Gelfand-Naimark-Segal representations
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1.12 Factorial and pure states1.13 Theorem (the Poisson kernel for the strip); 1.14 Corollary (the analytic version); 1.15 Theorem (the perturbation expansion theorem); 1.16 Corollary (the complex version); 1.17 Theorem (convergence on geometric vectors); 1.18 Proposition (the restricted C*-system); 2 Bounded derivations; Introduction; 2.1 Introduction to derivations; 2.2 The commutation relation ab - ba = 1; 2.3 Continuity of everywhere-defined derivations; 2.4 Quantum field-theoretic observations (some unbounded derivations); 2.5 Application to bounded derivations
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2.7 C*-dynamical systems and ground states3 Unbounded derivations; Introduction; 3.1 Definition of derivations; 3.2 Closability of derivations; 3.3 The domain of closed *-derivations; 3.4 Generators; 3.5 Unbounded derivations in commutative C*-algebras; 3.6 Transformation groups and unbounded derivations; 4 C*-dynamicaI systems; 4.0 Introduction; 4.1 Approximately inner C*-dynamics; 4.2 Ground states; 4.3 KMS states; 4.4 Bounded perturbations; 4.8 Continuous quantum systems; 4.5 UHF algebras and normal *-derivations; 4.6 Commutative normal *-derivations in UHF algebras; 4.7 Phase transitions
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ReferencesIndex
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English
Additional Edition:
ISBN 0-521-06021-4
Additional Edition:
ISBN 0-521-40096-1
Language:
English
