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Zusatztext "Sewell's book begins with a self-contained introduction to algebraic quantum theory (especially of infinite systems); and this! together with the fact that Sewell always develops only as much mathematics as he needs for his physics! means that his 300 page book provides a masterly overview of his field." ---Jeremy Butterfield! Philosophy of Science Informationen zum Autor Geoffrey Sewell Klappentext The quantum theory of macroscopic systems is a vast, ever-developing area of science that serves to relate the properties of complex physical objects to those of their constituent particles. Its essential challenge is that of finding the conceptual structures needed for the description of the various states of organization of many-particle quantum systems. In this book, Geoffrey Sewell provides a new approach to the subject, based on a "macrostatistical mechanics," which contrasts sharply with the standard microscopic treatments of many-body problems. Sewell begins by presenting the operator algebraic framework for the theory. He then undertakes a macrostatistical treatment of both equilibrium and nonequilibrium thermodynamics, which yields a major new characterization of a complete set of thermodynamic variables and a nonlinear generalization of the Onsager theory. The remainder of the book focuses on ordered and chaotic structures that arise in some key areas of condensed matter physics. This includes a general derivation of superconductive electrodynamics from the assumptions of off-diagonal long-range order, gauge covariance, and thermodynamic stability, which avoids the enormous complications of the microscopic treatments. Sewell also unveils a theoretical framework for phase transitions far from thermal equilibrium. Throughout, the mathematics is kept clear without sacrificing rigor. Representing a coherent approach to the vast problem of the emergence of macroscopic phenomena from quantum mechanics, this well-written book is addressed to physicists, mathematicians, and other scientists interested in quantum theory, statistical physics, thermodynamics, and general questions of order and chaos. Zusammenfassung The quantum theory of macroscopic systems is an area of science that serves to relate the properties of physical objects to those of their constituent particles. This book provides an approach, based on a 'macrostatistical mechanics', which contrasts with the standard microscopic treatments of many-body problems. Inhaltsverzeichnis Preface ix Notation xi Part I. The Algebraic Quantum Mechanical Framework and the Description of Order, Disorder and Irreversibility in Macroscopic Systems: Prospectus 1 Chapter 1. Introductory Discussion of Quantum Macrophysics 3 Chapter 2. The Generalised Quantum Mechanical Framework 7 2.1. Observables, States, Dynamics 8 2.2. Finite Quantum Systems 8 2.2.1. Uniqueness of the Representation 8 2.2.2. The Generic Model 10 2.2.3. The Algebraic Picture 13 2.3. Infinite Systems: Inequivalent Representations 15 2.3.1. The Representation o-(+) 15 2.3.2. The Representation o(-) 17 2.3.3. Inequivalence of o:(+-) 17 2.3.4. Other Inequivalent Representations 18 2.4. Operator Algebraic Interlude 18 2.4.1. Algebras: Basic Definitions and Properties 18 2.4.2. States and Representations 21 2.4.3. Automorphisms and Antiautomorphisms 24 2.4.4. Tensor Products 26 2.4.5. Quantum Dynamical Systems 27 2.4.6. Derivations of *-Algebras and Generators of Dynamical Groups 28 2.5. Algebraic Formulation of Infinite Systems 29 2.5.1. The General Scheme 29 2.5.2. Construction of the Lattice Model 32 2.5.3. Construction of the Continuum Model 34 2.6. The Physical Picture 39 2.6.1. Normal Folia as Local Modifications of Single States 39 2.6.2. Space-translationally Invariant States 39 2.6.3. Primary States have S...
