A Mathematical Introduction to Conformal Field Theory
Authors: Schottenloher, Martin
Free PreviewBuy this book
 About this book

The first part of this book gives a detailed, selfcontained and mathematically rigorous exposition of classical conformal symmetry in n dimensions and its quantization in two dimensions. In particular, the conformal groups are determined and the appearance of the Virasoro algebra in the context of the quantization of twodimensional conformal symmetry is explained via the classification of central extensions of Lie algebras and groups. The second part surveys some more advanced topics of conformal field theory, such as the representation theory of the Virasoro algebra, conformal symmetry within string theory, an axiomatic approach to Euclidean conformally covariant quantum field theory and a mathematical interpretation of the Verlinde formula in the context of moduli spaces of holomorphic vector bundles on a Riemann surface.
The substantially revised and enlarged second edition makes in particular the second part of the book more selfcontained and tutorial, with many more examples given. Furthermore, two new chapters on Wightman's axioms for quantum field theory and vertex algebras broaden the survey of advanced topics. An outlook making the connection with most recent developments has also been added.  Reviews

From the reviews of the second edition:
"The book under review is the second … edition of the original text, thereby reflecting various recent developments in the field during the past ten years, on the one hand, and making especially the physics part of the notes more detailed, selfcontained and tutorial on the other. … this highly appreciated mediator between contemporary mathematics and physical quantum field theory has grown into an even more valuable source for students, teachers, and active researchers in this fascinating area of modern science." (Werner Kleinert, Zentralblatt MATH, Vol. 1161, 2009)
“The second edition of this classical introduction to conformal field theory for a mathematically oriented audience has been substantially revised and expanded … . many new examples and statements have been included throughout the whole text. … Completeness, the extremely clear exposition and wellchosen references at the end of each chapter make this introduction an unmissable reference for the mathematician aiming to learn the basics of conformal field theory.” (Domenico Fiorenza, Mathematical Reviews, Issue 2011 a)
 Table of contents (12 chapters)


Conformal Transformations and Conformal Killing Fields
Pages 721

The Conformal Group
Pages 2338

Central Extensions of Groups
Pages 3962

Central Extensions of Lie Algebras and Bargmann’s Theorem
Pages 6373

The Virasoro Algebra
Pages 7585

Table of contents (12 chapters)
 Download Preface 1 PDF (141.1 KB)
 Download Sample pages 2 PDF (379.2 KB)
 Download Table of contents PDF (112.6 KB)
Recommended for you
Bibliographic Information
 Bibliographic Information

 Book Title
 A Mathematical Introduction to Conformal Field Theory
 Authors

 Martin Schottenloher
 Series Title
 Lecture Notes in Physics
 Series Volume
 759
 Copyright
 2008
 Publisher
 SpringerVerlag Berlin Heidelberg
 Copyright Holder
 SpringerVerlag Berlin Heidelberg
 eBook ISBN
 9783540686286
 DOI
 10.1007/9783540686286
 Hardcover ISBN
 9783540686255
 Softcover ISBN
 9783642088155
 Series ISSN
 00758450
 Edition Number
 2
 Number of Pages
 XV, 249
 Additional Information
 Originally published as vol 43 in the series: Lecture Notes in Physics Monographs
 Topics