A Mathematical Introduction to Conformal Field 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...

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Main Author: Schottenloher, Martin. (Author, http://id.loc.gov/vocabulary/relators/aut)
Corporate Author: SpringerLink (Online service)
Language:English
Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2008.
Edition:2nd ed. 2008.
Series:Lecture Notes in Physics, 759
Subjects:
Online Access:https://doi.org/10.1007/978-3-540-68628-6
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.