A Mathematical Introduction to Conformal Field Theory

• Main Author: Schottenloher, M. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2008.
• Edition: 2.
• Series: Lecture Notes in Physics, 759
• Subjects: Physics.; Algebra.; Global analysis (Mathematics).; Manifolds (Mathematics).; Quantum field theory.; String theory.; Elementary particles (Physics).; Mathematical Methods in Physics.; Global Analysis and Analysis on Manifolds.; Elementary Particles, Quantum Field Theory.; Quantum Field Theories, String Theory.

The first part of this book gives a detailed, self-contained 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...

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.