Vertex Operators In Mathematics And Physics
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Vertex Operators In Mathematics And Physics
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Author : J. Lepowsky
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-08
Vertex Operators In Mathematics And Physics written by J. 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 2013-03-08 with Science categories.
James Lepowsky t The search for symmetry in nature has for a long time provided representation theory with perhaps its chief motivation. According to the standard approach of Lie theory, one looks for infinitesimal symmetry -- Lie algebras of operators or concrete realizations of abstract Lie algebras. A central theme in this volume is the construction of affine Lie algebras using formal differential operators called vertex operators, which originally appeared in the dual-string theory. Since the precise description of vertex operators, in both mathematical and physical settings, requires a fair amount of notation, we do not attempt it in this introduction. Instead we refer the reader to the papers of Mandelstam, Goddard-Olive, Lepowsky-Wilson and Frenkel-Lepowsky-Meurman. We have tried to maintain consistency of terminology and to some extent notation in the articles herein. To help the reader we shall review some of the terminology. We also thought it might be useful to supplement an earlier fairly detailed exposition of ours [37] with a brief historical account of vertex operators in mathematics and their connection with affine algebras. Since we were involved in the development of the subject, the reader should be advised that what follows reflects our own understanding. For another view, see [29].1 t Partially supported by the National Science Foundation through the Mathematical Sciences Research Institute and NSF Grant MCS 83-01664. 1 We would like to thank Igor Frenkel for his valuable comments on the first draft of this introduction.
Vertex Operators In Mathematics And Physics
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Author : J. Lepowsky
language : en
Publisher:
Release Date : 2014-01-15
Vertex Operators In Mathematics And Physics written by J. Lepowsky and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Vertex Operator Algebras In Mathematics And Physics
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Author : Stephen Berman
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Vertex Operator Algebras In Mathematics And Physics written by Stephen Berman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
Vertex operator algebras are a class of algebras underlying a number of recent constructions, results, and themes in mathematics. These algebras can be understood as ''string-theoretic analogues'' of Lie algebras and of commutative associative algebras. They play fundamental roles in some of the most active research areas in mathematics and physics. Much recent progress in both physics and mathematics has benefited from cross-pollination between the physical and mathematical points of view. This book presents the proceedings from the workshop, ''Vertex Operator Algebras in Mathematics and Physics'', held at The Fields Institute. It consists of papers based on many of the talks given at the conference by leading experts in the algebraic, geometric, and physical aspects of vertex operator algebra theory. The book is suitable for graduate students and research mathematicians interested in the major themes and important developments on the frontier of research in vertex operator algebra theory and its applications in mathematics and physics.
Vertex Operator Algebras And The Monster
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Author : Igor Frenkel
language : en
Publisher: Academic Press
Release Date : 1989-05-01
Vertex Operator Algebras And The Monster written by Igor Frenkel and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-05-01 with Mathematics categories.
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."
Vertex Operators In Mathematics And Physics
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Author : Isadore Manuel Singer
language : en
Publisher:
Release Date : 1985-01-01
Vertex Operators In Mathematics And Physics written by Isadore Manuel Singer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-01-01 with Algèbres non associatives - Congrès categories.
Vertex Operator Algebras In Mathematics And Physics
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Author : Stephen Berman
language : en
Publisher:
Release Date : 2003
Vertex Operator Algebras In Mathematics And Physics written by Stephen Berman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematical physics categories.
This book presents the proceedings from the workshop, "Vertex Operator Algebras in Mathematics and Physics", held at The Fields Institute. It consists of papers based on many of the talks given at the conference by leading experts in the algebraic, geometric, and physical aspects of vertex operator algebra theory. The book is suitable for graduate students and research mathematicians interested in the major themes and important developments on the frontier of research in vertex operator algebra theory and its applications in mathematics and physics.
Vertex Algebras And Algebraic Curves
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Author : Edward Frenkel
language : en
Publisher: American Mathematical Soc.
Release Date : 2004-08-25
Vertex Algebras And Algebraic Curves written by Edward Frenkel and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-08-25 with Mathematics categories.
Vertex algebras are algebraic objects that encapsulate the concept of operator product expansion from two-dimensional conformal field theory. Vertex algebras are fast becoming ubiquitous in many areas of modern mathematics, with applications to representation theory, algebraic geometry, the theory of finite groups, modular functions, topology, integrable systems, and combinatorics. This book is an introduction to the theory of vertex algebras with a particular emphasis on the relationship with the geometry of algebraic curves. The notion of a vertex algebra is introduced in a coordinate-independent way, so that vertex operators become well defined on arbitrary smooth algebraic curves, possibly equipped with additional data, such as a vector bundle. Vertex algebras then appear as the algebraic objects encoding the geometric structure of various moduli spaces associated with algebraic curves. Therefore they may be used to give a geometric interpretation of various questions of representation theory. The book contains many original results, introduces important new concepts, and brings new insights into the theory of vertex algebras. The authors have made a great effort to make the book self-contained and accessible to readers of all backgrounds. Reviewers of the first edition anticipated that it would have a long-lasting influence on this exciting field of mathematics and would be very useful for graduate students and researchers interested in the subject. This second edition, substantially improved and expanded, includes several new topics, in particular an introduction to the Beilinson-Drinfeld theory of factorization algebras and the geometric Langlands correspondence.
String Path Integral Realization Of Vertex Operator Algebras
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Author : Haruo Tsukada
language : en
Publisher: American Mathematical Soc.
Release Date : 1991
String Path Integral Realization Of Vertex Operator Algebras written by Haruo Tsukada and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.
We establish relations between vertex operator algebras in mathematics and string path integrals in physics. In particular, we construct the basic representations of affine Lie algebras of [italic capitals]ÂD̂Ê-type using a method of string path integrals.
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.
Generalized Vertex Algebras And Relative Vertex Operators
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Author : Chongying Dong
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Generalized Vertex Algebras And Relative Vertex Operators written by Chongying Dong 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 the past few years, vertex operator algebra theory has been growing both in intrinsic interest and in the scope of its interconnections with areas of mathematics and physics. The structure and representation theory of vertex operator algebras is deeply related to such subjects as monstrous moonshine, conformal field theory and braid group theory. Vertex operator algebras are the mathematical counterpart of chiral algebras in conformal field theory. In the Introduction which follows, we sketch some of the main themes in the historical development and mathematical and physical motivations of these ideas, and some of the current issues. Given a vertex operator algebra, it is important to consider not only its modules (representations) but also intertwining operators among the mod ules. Matrix coefficients of compositions of these operators, corresponding to certain kinds of correlation functions in conformal field theory, lead natu rally to braid group representations. In the specialbut important case when these braid group representations are one-dimensional, one can combine the modules and intertwining operators with the algebra to form a structure satisfying axioms fairly close to those for a vertex operator algebra. These are the structures which form the main theme of this monograph. Another treatment of similar structures has been given by Feingold, Frenkel and Ries (see the reference [FFR] in the Bibliography), and in fact the material de veloped in the present work has close connections with much work of other people, as we explain in the Introduction and throughout the text.