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Author: Tirthankar Bhattacharyya
Publisher: Birkhäuser
ISBN: 3319181823
Category : Mathematics
Languages : en
Pages : 202
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Book Description
This volume gathers contributions from the International Workshop on Operator Theory and Its Applications (IWOTA) held in Bangalore, India, in December 2013. All articles were written by experts and cover a broad range of original material at the cutting edge of operator theory and its applications. Topics include multivariable operator theory, operator theory on indefinite metric spaces (Krein and Pontryagin spaces) and its applications, spectral theory with applications to differential operators, the geometry of Banach spaces, scattering and time varying linear systems, and wavelets and coherent states.
Author: Tirthankar Bhattacharyya
Publisher: Birkhäuser
ISBN: 3319181823
Category : Mathematics
Languages : en
Pages : 202
Get Book
Book Description
This volume gathers contributions from the International Workshop on Operator Theory and Its Applications (IWOTA) held in Bangalore, India, in December 2013. All articles were written by experts and cover a broad range of original material at the cutting edge of operator theory and its applications. Topics include multivariable operator theory, operator theory on indefinite metric spaces (Krein and Pontryagin spaces) and its applications, spectral theory with applications to differential operators, the geometry of Banach spaces, scattering and time varying linear systems, and wavelets and coherent states.
Author: Masamichi Takesaki
Publisher: Springer Science & Business Media
ISBN: 1461261880
Category : Mathematics
Languages : en
Pages : 424
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Book Description
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.
Author: Ola Bratteli
Publisher: Springer Science & Business Media
ISBN: 9783540170938
Category : Mathematics
Languages : en
Pages : 528
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Book Description
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.
Author: Ola Bratteli
Publisher: Springer Science & Business Media
ISBN:
Category : Mathematics
Languages : en
Pages : 544
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Book Description
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.
Author: Richard Herman
Publisher: CRC Press
ISBN: 1439863512
Category : Mathematics
Languages : en
Pages : 336
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Book Description
This volume records the proceedings of an international conference that explored recent developments and the interaction between mathematical theory and physical phenomena.
Author: Palle E. T. Jørgensen
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 564
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Book Description
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.
Author: James Lepowsky
Publisher: Springer Science & Business Media
ISBN: 0817681868
Category : Mathematics
Languages : en
Pages : 330
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Book Description
* 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.
Author: Ola Bratteli
Publisher: Springer Science & Business Media
ISBN: 366202313X
Category : Mathematics
Languages : en
Pages : 503
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Book Description
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.
Author: Ola Bratteli
Publisher: Springer Science & Business Media
ISBN: 3662034441
Category : Science
Languages : en
Pages : 525
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Book Description
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.
Author: Igor Frenkel
Publisher: Academic Press
ISBN: 0080874541
Category : Mathematics
Languages : en
Pages : 563
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Book Description
This work is motivated by and develops connections between several branches of mathematics and physics--the theories of Lie algebras, finite groups and modular functions in mathematics, and string theory in physics. The first part of the book presents a new mathematical theory of vertex operator algebras, the algebraic counterpart of two-dimensional holomorphic conformal quantum field theory. The remaining part constructs the Monster finite simple group as the automorphism group of a very special vertex operator algebra, called the "moonshine module" because of its relevance to "monstrous moonshine."
