Causal Nets Of Operator Algebras
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Causal Nets Of Operator Algebras
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Author : Hellmut Baumgärtel
language : en
Publisher: De Gruyter Akademie Forschung
Release Date : 1992
Causal Nets Of Operator Algebras written by Hellmut Baumgärtel and has been published by De Gruyter Akademie Forschung this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematical physics categories.
For advanced students in mathematics and mathematicians, as well as theoretical physicists, this volume presents the theory of nets of operator algebras, in particular nets connected with a causality condition. Such nets appear in mathematical formulations of quantum statistical mechanics and of quantum field theory. In this volume, the emphasis lies on nets which are linked with the algebraic approach to quantum field theory. Assumes a basic knowledge of functional analysis, in particular in the field of operator algebras. Annotation copyright by Book News, Inc., Portland, OR
Notes On Pertubations Of Causal Nets Of Operator Algebras
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Author : Manfred Wollenberg
language : de
Publisher:
Release Date : 1992
Notes On Pertubations Of Causal Nets Of Operator Algebras written by Manfred Wollenberg and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with categories.
Introduction To Operator Algebras
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Author : Bing-Ren Li
language : en
Publisher: World Scientific
Release Date : 1992
Introduction To Operator Algebras written by Bing-Ren Li and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.
This book is an introductory text on one of the most important fields of Mathematics, the theory of operator algebras. It offers a readable exposition of the basic concepts, techniques, structures and important results of operator algebras. Written in a self-contained manner, with an emphasis on understanding, it serves as an ideal text for graduate students.
Operator Algebras And Quantum Statistical Mechanics
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Author : Ola Bratteli
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Operator Algebras And Quantum Statistical Mechanics written by Ola Bratteli and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Operatoralgebraic Methods In Quantum Field Theory
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Author : Hellmut Baumgärtel
language : en
Publisher: De Gruyter Akademie Forschung
Release Date : 1995
Operatoralgebraic Methods In Quantum Field Theory written by Hellmut Baumgärtel and has been published by De Gruyter Akademie Forschung this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.
In the course of lectures, held from summer 1993 up to summer 1994 at the Humboldt University of Berlin (SS 93), the Technical University of Berlin (WS 93/94) and the University of Potsdam (SS 94) the author presents basic operatoralgebraic material which is necessary to establish basic concepts of the algebraic quantum field theory as well as to get essential results in this field. The original ansatz of R. Haag (and others) started with the "working hypothesis" of a net of algebras of local observables. The aim of the lectures is to show that the success of this ansatz is strongly connected with deep results in the theory of operator algebras. Some characteristic mutual relations are described. Key words are "Vacuum representations on the four-dimensional Minkowski space and on the unit sphere, DHR-superselection theory, field algebra", and others. The emphasis is to make the material presented clear and readable without missing depth. The hope is to convince the reader of the beauty and stringency of this theory. While the first part of the book describes vacuum representations on the four-dimensional Minkowski space, the second part deals with the so-called DHR-superselection theory, firstly for the automorphism case and secondly for the general case. The constructions of the field algebra and the symmetry group are included. Finally, vacuum representations on the unit sphere S1 are discussed.
Operator Algebras And Quantum Statistical Mechanics 1
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Author : Ola Bratteli
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Operator Algebras And Quantum Statistical Mechanics 1 written by Ola Bratteli and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Technology & Engineering categories.
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.
Theory Of Operator Algebras I
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Author : Masamichi Takesaki
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Theory Of Operator Algebras I written by Masamichi Takesaki and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Mathematics for infinite dimensional objects is becoming more and more important today both in theory and application. Rings of operators, renamed von Neumann algebras by J. Dixmier, were first introduced by J. von Neumann fifty years ago, 1929, in [254] with his grand aim of giving a sound founda tion to mathematical sciences of infinite nature. J. von Neumann and his collaborator F. J. Murray laid down the foundation for this new field of mathematics, operator algebras, in a series of papers, [240], [241], [242], [257] and [259], during the period of the 1930s and early in the 1940s. In the introduction to this series of investigations, they stated Their solution 1 {to the problems of understanding rings of operators) seems to be essential for the further advance of abstract operator theory in Hilbert space under several aspects. First, the formal calculus with operator-rings leads to them. Second, our attempts to generalize the theory of unitary group-representations essentially beyond their classical frame have always been blocked by the unsolved questions connected with these problems. Third, various aspects of the quantum mechanical formalism suggest strongly the elucidation of this subject. Fourth, the knowledge obtained in these investigations gives an approach to a class of abstract algebras without a finite basis, which seems to differ essentially from all types hitherto investigated. Since then there has appeared a large volume of literature, and a great deal of progress has been achieved by many mathematicians.
Operator Algebras And Applications
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Author : A. Katavolos
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Operator Algebras And Applications written by A. Katavolos and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
During the last few years, the theory of operator algebras, particularly non-self-adjoint operator algebras, has evolved dramatically, experiencing both international growth and interfacing with other important areas. The present volume presents a survey of some of the latest developments in the field in a form that is detailed enough to be accessible to advanced graduate students as well as researchers in the field. Among the topics treated are: operator spaces, Hilbert modules, limit algebras, reflexive algebras and subspaces, relations to basis theory, C* algebraic quantum groups, endomorphisms of operator algebras, conditional expectations and projection maps, and applications, particularly to wavelet theory. The volume also features an historical paper offering a new approach to the Pythagoreans' discovery of irrational numbers.
Recent Advances In Operator Theory And Operator Algebras
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Author : Hari Bercovici
language : en
Publisher: CRC Press
Release Date : 2017-08-07
Recent Advances In Operator Theory And Operator Algebras written by Hari Bercovici and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-07 with Mathematics categories.
This book will contain lectures given by four eminent speakers at the Recent Advances in Operator Theory and Operator Algebras conference held at the Indian Statistical Institute, Bangalore, India in 2014. The main aim of this book is to bring together various results in one place with cogent introduction and references for further study.
Fundamentals Of The Theory Of Operator Algebras
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Author : KADISON
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Fundamentals Of The Theory Of Operator Algebras written by KADISON and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
These volumes are companions to the treatise; "Fundamentals of the Theory of Operator Algebras," which appeared as Volume 100 - I and II in the series, Pure and Applied Mathematics, published by Academic Press in 1983 and 1986, respectively. As stated in the preface to those volumes, "Their primary goal is to teach the sub ject and lead the reader to the point where the vast recent research literature, both in the subject proper and in its many applications, becomes accessible." No attempt was made to be encyclopcedic; the choice of material was made from among the fundamentals of what may be called the "classical" theory of operator algebras. By way of supplementing the topics selected for presentation in "Fundamentals," a substantial list of exercises comprises the last section of each chapter. An equally important purpose of those exer cises is to develop "hand-on" skills in use ofthe techniques appearing in the text. As a consequence, each exercise was carefully designed to depend only on the material that precedes it, and separated into segments each of which is realistically capable of solution by an at tentive, diligent, well-motivated reader.