Operator Algebras And Quantum Field Theory

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C Algebras And W Algebras

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Author : Shoichiro Sakai
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

C Algebras And W Algebras written by Shoichiro Sakai 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.

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." (Math. Reviews) "In theory, this book can be read by a well-trained third-year graduate student - but the reader had better have a great deal of mathematical sophistication. The specialist in this and allied areas will find the wealth of recent results and new approaches throughout the text especially rewarding." (American Scientist) "The title of this book at once suggests comparison with the two volumes of Dixmier and the fact that one can seriously make this comparison indicates that it is a far more substantial work that others on this subject which have recently appeared"(BLMSoc)

Operator Algebras And Quantum Statistical Mechanics 1

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Author : Ola Bratteli
language : en
Publisher: Springer Science & Business Media
Release Date : 1987-05-27

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 1987-05-27 with Mathematics categories.

This is the first of two volumes presenting the theory of operator algebras with applications to quantum statistical mechanics. The authors' approach to the operator theory is to a large extent governed by the dictates of the physical applications. The book is self-contained and most proofs are presented in detail, which makes it a useful text for students with a knowledge of basic functional analysis. The introductory chapter surveys the history and justification of algebraic techniques in statistical physics and outlines the applications that have been made. The second edition contains new and improved results. The principal changes include: A more comprehensive discussion of dissipative operators and analytic elements; the positive resolution of the question of whether maximal orthogonal probability measure on the state space of C-algebra were automatically maximal along all the probability measures on the space.

Introduction To Algebraic Quantum Field Theory

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Author : S.S. Horuzhy
language : en
Publisher: Springer Science & Business Media
Release Date : 1990-06-30

Introduction To Algebraic Quantum Field Theory written by S.S. Horuzhy 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 1990-06-30 with Science categories.

'Et moi, ... , si j'avait su comment en revenir, One service mathematics has rendered the human race. It has put common sense back je n'y serais point aile.' Jules Verne where it belongs, on the topmost shel.f next to the dusty canister labelled 'discarded non­ The series is divergent; therefore we may be sense'. Eric T. Bell able to do something with it. o. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non­ linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com­ puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

Introduction To Vertex Operator Algebras And Their Representations

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Author : James Lepowsky
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Introduction To Vertex Operator Algebras And Their Representations written by James Lepowsky 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.

* Introduces the fundamental theory of vertex operator algebras and its basic techniques and examples. * Begins with a detailed presentation of the theoretical foundations and proceeds to a range of applications. * Includes a number of new, original results and brings fresh perspective to important works of many other researchers in algebra, lie theory, representation theory, string theory, quantum field theory, and other areas of math and physics.

Quantum Symmetries On Operator Algebras

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Author : David Emrys Evans
language : en
Publisher:
Release Date : 1998

Quantum Symmetries On Operator Algebras written by David Emrys Evans and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.

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 and connections with different areas in both pure mathematics (foliations, index theory, K-theory, cyclic homology, affine Kac--Moody algebras, quantum groups, low dimensional topology) and mathematical physics (integrable theories, statistical mechanics, conformal field theories and the string theories of elementary particles). The theory of operator algebras 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 Vaughan Jones of subfactor theory and remarkable connections were found with knot theory, 3-manifolds, quantum groups and integrable systems in statistical mechanics and conformal field theory. The purpose of this book, one of the first in the area, is to look at these combinatorial-algebraic developments from the perspective of operator algebras; to bring the reader to the frontline of research with the minimum of prerequisites from classical theory.

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.

C Algebras And Operator Theory

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Author : Gerald J. Murphy
language : en
Publisher: Academic Press
Release Date : 2014-06-28

C Algebras And Operator Theory written by Gerald J. Murphy and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-28 with Mathematics categories.

This book constitutes a first- or second-year graduate course in operator theory. It is a field that has great importance for other areas of mathematics and physics, such as algebraic topology, differential geometry, and quantum mechanics. It assumes a basic knowledge in functional analysis but no prior acquaintance with operator theory is required.

Operator Algebras And Quantum Field Theory

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Author : Sergio Doplicher
language : en
Publisher:
Release Date : 1997

Operator Algebras And Quantum Field Theory written by Sergio Doplicher and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.

A collection of papers presented at a conference in Rome on operator algebras and quantum field theory. Invited contributions on noncommutative dynamical systems, the Baum-Cohnes and the Novikov conjecture, the Atiyah-Singer index theorem, and Banach Space aspects are included.

Theory Of Operator Algebras I

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Author : M. Takesaki
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-11-20

Theory Of Operator Algebras I written by M. 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 2001-11-20 with Mathematics categories.

Since its inception by von Neumann 70 years ago, the theory of operator algebras has become a rapidly developing area of importance for the understanding of many areas of mathematics and theoretical physics. Accessible to the non-specialist, this first part of a three-volume treatise provides a clear, carefully written survey that emphasizes the theory's analytical and topological aspects.

Reality And Measurement In Algebraic Quantum Theory

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Author : Masanao Ozawa
language : en
Publisher: Springer
Release Date : 2018-11-29

Reality And Measurement In Algebraic Quantum Theory written by Masanao Ozawa and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-29 with Mathematics categories.

This volume contains papers based on presentations at the “Nagoya Winter Workshop 2015: Reality and Measurement in Algebraic Quantum Theory (NWW 2015)”, held in Nagoya, Japan, in March 2015. The foundations of quantum theory have been a source of mysteries, puzzles, and confusions, and have encouraged innovations in mathematical languages to describe, analyze, and delineate this wonderland. Both ontological and epistemological questions about quantum reality and measurement have been placed in the center of the mysteries explored originally by Bohr, Heisenberg, Einstein, and Schrödinger. This volume describes how those traditional problems are nowadays explored from the most advanced perspectives. It includes new research results in quantum information theory, quantum measurement theory, information thermodynamics, operator algebraic and category theoretical foundations of quantum theory, and the interplay between experimental and theoretical investigations on the uncertainty principle. This book is suitable for a broad audience of mathematicians, theoretical and experimental physicists, and philosophers of science.