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Operator Algebras And Quantum Statistical Mechanics 1
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Book Synopsis Operator Algebras and Quantum Statistical Mechanics 1 by : Ola Bratteli
Download or read book Operator Algebras and Quantum Statistical Mechanics 1 written by Ola Bratteli and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book we describe the elementary theory of operator algebras and parts of the advanced theory which are of relevance, or potentially of relevance, to mathematical physics. Subsequently we describe various applications to quantum statistical mechanics. At the outset of this project we intended to cover this material in one volume but in the course of develop ment it was realized that this would entail the omission ofvarious interesting topics or details. Consequently the book was split into two volumes, the first devoted to the general theory of operator algebras and the second to the applications. This splitting into theory and applications is conventional but somewhat arbitrary. In the last 15-20 years mathematical physicists have realized the importance of operator algebras and their states and automorphisms for problems of field theory and statistical mechanics. But the theory of 20 years aga was largely developed for the analysis of group representations and it was inadequate for many physical applications. Thus after a short honey moon period in which the new found tools of the extant theory were applied to the most amenable problems a longer and more interesting period ensued in which mathematical physicists were forced to redevelop the theory in relevant directions. New concepts were introduced, e. g. asymptotic abelian ness and KMS states, new techniques applied, e. g. the Choquet theory of barycentric decomposition for states, and new structural results obtained, e. g. the existence of a continuum of nonisomorphic type-three factors.
Book Synopsis Operator Algebras and Quantum Statistical Mechanics by : Ola Bratteli
Download or read book Operator Algebras and Quantum Statistical Mechanics written by Ola Bratteli and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 503 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book we describe the elementary theory of operator algebras and parts of the advanced theory which are of relevance, or potentially of relevance, to mathematical physics. Subsequently we describe various applications to quantum statistical mechanics. At the outset of this project we intended to cover this material in one volume but in the course of develop ment it was realized that this would entail the omission of various interesting topics or details. Consequently the book was split into two volumes, the first devoted to the general theory of operator algebras and the second to the applications. This splitting into theory and applications is conventional but somewhat arbitrary. In the last 15-20 years mathematical physicists have realized the importance of operator algebras and their states and automorphisms for problems offield theory and statistical mechanics. But the theory of 20 years ago was largely developed for the analysis of group representations and it was inadequate for many physical applications. Thus after a short honey moon period in which the new found tools of the extant theory were applied to the most amenable problems a longer and more interesting period ensued in which mathematical physicists were forced to redevelop the theory in relevant directions. New concepts were introduced, e. g. asymptotic abelian ness and KMS states, new techniques applied, e. g. the Choquet theory of barycentric decomposition for states, and new structural results obtained, e. g. the existence of a continuum of nonisomorphic type-three factors.
Book Synopsis Operator Algebras and Quantum Statistical Mechanics 1 by : Ola Bratteli
Download or read book Operator Algebras and Quantum Statistical Mechanics 1 written by Ola Bratteli and published by Springer. This book was released on 2010-10-19 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book we describe the elementary theory of operator algebras and parts of the advanced theory which are of relevance, or potentially of relevance, to mathematical physics. Subsequently we describe various applications to quantum statistical mechanics. At the outset of this project we intended to cover this material in one volume but in the course of develop ment it was realized that this would entail the omission ofvarious interesting topics or details. Consequently the book was split into two volumes, the first devoted to the general theory of operator algebras and the second to the applications. This splitting into theory and applications is conventional but somewhat arbitrary. In the last 15-20 years mathematical physicists have realized the importance of operator algebras and their states and automorphisms for problems of field theory and statistical mechanics. But the theory of 20 years aga was largely developed for the analysis of group representations and it was inadequate for many physical applications. Thus after a short honey moon period in which the new found tools of the extant theory were applied to the most amenable problems a longer and more interesting period ensued in which mathematical physicists were forced to redevelop the theory in relevant directions. New concepts were introduced, e. g. asymptotic abelian ness and KMS states, new techniques applied, e. g. the Choquet theory of barycentric decomposition for states, and new structural results obtained, e. g. the existence of a continuum of nonisomorphic type-three factors.
Book Synopsis Operator Algebras and Quantum Statistical Mechanics by : Ola Bratteli
Download or read book Operator Algebras and Quantum Statistical Mechanics written by Ola Bratteli and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 525 pages. Available in PDF, EPUB and Kindle. Book excerpt: For almost two decades, this has been the classical textbook on applications of operator algebra theory to quantum statistical physics. Major changes in the new edition relate to Bose-Einstein condensation, the dynamics of the X-Y model and questions on phase transitions.
Book Synopsis Operator Algebras and Quantum Statistical Mechanics by : Ola Bratteli
Download or read book Operator Algebras and Quantum Statistical Mechanics written by Ola Bratteli and published by Springer Science & Business Media. This book was released on 1979 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: For almost two decades, this has been the classical textbook on applications of operator algebra theory to quantum statistical physics. Major changes in the new edition relate to Bose-Einstein condensation, the dynamics of the X-Y model and questions on phase transitions.
Book Synopsis Operator Algebras and Quantum Statistical Mechanics by : Ola Bratteli
Download or read book Operator Algebras and Quantum Statistical Mechanics written by Ola Bratteli and published by Springer Science & Business Media. This book was released on 2003-01-09 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: For almost two decades, this has been the classical textbook on applications of operator algebra theory to quantum statistical physics. Major changes in the new edition relate to Bose-Einstein condensation, the dynamics of the X-Y model and questions on phase transitions.
Book Synopsis Operator Algebras and Quantum Statistical Mechanics by : Ola Bratteli
Download or read book Operator Algebras and Quantum Statistical Mechanics written by Ola Bratteli and published by . This book was released on 1987 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Operator Algebras and Quantum Statistical Mechanics II by : Ola Bratteli
Download or read book Operator Algebras and Quantum Statistical Mechanics II written by Ola Bratteli and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: For almost two decades, this has been the classical textbook on applications of operator algebra theory to quantum statistical physics. Major changes in the new edition relate to Bose-Einstein condensation, the dynamics of the X-Y model and questions on phase transitions.
Book Synopsis Operator Algebras and Quantum Statistical Mechanics by : Ola Bratteli
Download or read book Operator Algebras and Quantum Statistical Mechanics written by Ola Bratteli and published by . This book was released on 1979 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis C*-Algebras and W*-Algebras by : Shoichiro Sakai
Download or read book C*-Algebras and W*-Algebras written by Shoichiro Sakai and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "This book is an excellent and comprehensive survey of the theory of von Neumann algebras. It includes all the fundamental results of the subject, and is a valuable reference for both the beginner and the expert." Mathematical Reviews
Book Synopsis Operator Algebras and Quantum Statistical Mechanics by : Ola Bratteli
Download or read book Operator Algebras and Quantum Statistical Mechanics written by Ola Bratteli and published by . This book was released on 1984 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Statistical Mechanics of Lattice Systems by : David Lavis
Download or read book Statistical Mechanics of Lattice Systems written by David Lavis and published by Springer Science & Business Media. This book was released on 1999-03-08 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most of the interesting and difficult problems in statistical mechanics arise when the constituent particles of the system interact with each other with pair or multipartiele energies. The types of behaviour which occur in systems because of these interactions are referred to as cooperative phenomena giving rise in many cases to phase transitions. This book and its companion volume (Lavis and Bell 1999, referred to in the text simply as Volume 1) are princi pally concerned with phase transitions in lattice systems. Due mainly to the insights gained from scaling theory and renormalization group methods, this subject has developed very rapidly over the last thirty years. ' In our choice of topics we have tried to present a good range of fundamental theory and of applications, some of which reflect our own interests. A broad division of material can be made between exact results and ap proximation methods. We have found it appropriate to inelude some of our discussion of exact results in this volume and some in Volume 1. Apart from this much of the discussion in Volume 1 is concerned with mean-field theory. Although this is known not to give reliable results elose to a critical region, it often provides a good qualitative picture for phase diagrams as a whole. For complicated systems some kind of mean-field method is often the only tractable method available. In this volume our main concern is with scaling theory, algebraic methods and the renormalization group.
Book Synopsis Operator algebras and quantum statistical mechanics by : Ola Bratteli
Download or read book Operator algebras and quantum statistical mechanics written by Ola Bratteli and published by . This book was released on 1981 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Foundations of Quantum Theory by : Klaas Landsman
Download or read book Foundations of Quantum Theory written by Klaas Landsman and published by . This book was released on 2020-10-09 with total page 880 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies the foundations of quantum theory through its relationship to classical physics. This idea goes back to the Copenhagen Interpretation (in the original version due to Bohr and Heisenberg), which the author relates to the mathematical formalism of operator algebras originally created by von Neumann. The book therefore includes comprehensive appendices on functional analysis and C*-algebras, as well as a briefer one on logic, category theory, and topos theory. Matters of foundational as well as mathematical interest that are covered in detail include symmetry (and its "spontaneous" breaking), the measurement problem, the Kochen-Specker, Free Will, and Bell Theorems, the Kadison-Singer conjecture, quantization, indistinguishable particles, the quantum theory of large systems, and quantum logic, the latter in connection with the topos approach to quantum theory. This work was published by Saint Philip Street Press pursuant to a Creative Commons license permitting commercial use. All rights not granted by the work's license are retained by the author or authors.
Book Synopsis Operator Algebras and Quantum Statistical Mechanics Ii by : Ola Bratteli
Download or read book Operator Algebras and Quantum Statistical Mechanics Ii written by Ola Bratteli and published by . This book was released on 1981 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Quantum Symmetries on Operator Algebras by : David Emrys Evans
Download or read book Quantum Symmetries on Operator Algebras written by David Emrys Evans and published by . This book was released on 1998 with total page 854 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last 20 years, the study of operator algebras has developed from a branch of functional analysis to a central field of mathematics with applications in both pure mathematics and mathematical physics. The theory was initiated by von Neumann and Murray as a tool for studying group representations and as a framework for quantum mechanics, and has since kept in touch with its roots in physics as a framework for quantum statistical mechanics and the formalism of algebraic quantum field theory. However, in 1981, the study of operator algebras took a new turn with the introduction by Vaughn Jones of subfactor theory, leading to remarkable connections with knot theory, 3-manifolds, quantum groups, and integrable systems in statistical mechanics and conformal field theory. This book, one of the first in the area, looks at these combinatorial-algebraic developments from the perspective of operator algebras. With minimal prerequisites from classical theory, it brings the reader to the forefront of research.
Book Synopsis Operator Algebras and Mathematical Physics by : Palle E. T. Jørgensen
Download or read book Operator Algebras and Mathematical Physics written by Palle E. T. Jørgensen and published by . This book was released on 1987 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains papers presented at the University of Iowa 1985 Summer Conference in honor of H.-J. Borchers, N. M. Hugenholtz, R. V. Kadison, and D. Kastler and gives a systematic, up-to-date treatment of the fruitful interaction that the last two decades have brought between operator algebras and mathematical physics. Special attention is paid to an overview of the algebraic approach to quantum field theory and in particular, to quantum statistical mechanics. More than half the papers culminate with a presentation of new results which have not appeared previously in journals, and with a few exceptions, these new results are presented with complete proofs. This book is addressed to graduate students and researchers working in a broad spectrum of areas in mathematics and mathematical physics. Functional analysis, operator algebras, operator theory, differential geometry, cyclic cohomology, $K$-theory, and index theory are applied to questions in the quantum theory of fields and statistical mechanics. The individual papers are self-contained, but the reader should have some familiarity with the basic concepts of functional analysis and operator theory, although no physics background is assumed.
