Table of Contents

Mathematical Preliminaries.- Conformal Transformations and Conformal Killing Fields.- The Conformal Group.- Central Extensions of Groups.- Central Extensions of Lie Algebras and Bargmann’s Theorem.- The Virasoro Algebra.- First Steps Toward Conformal Field Theory.- Representation Theory of the Virasoro Algebra.- String Theory as a Conformal Field Theory.- Axioms of Relativistic Quantum Field Theory.- Foundations of Two-Dimensional Conformal Quantum Field Theory.- Vertex Algebras.- Mathematical Aspects of the Verlinde Formula.- Appendix A.

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, self-contained 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 well-chosen 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)