Schottenloher A Mathematical Introduction to Conformal Field Theory

Based on a Series of Lectures given at the Mathematisches Institut der Universität Hamburg
Erscheinungsjahr 2008
ISBN: 978-3-540-70690-8
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 43, 144 Seiten, eBook

Reihe: Lecture Notes in Physics Monographs

Part I gives a detailed, self-contained and mathematically rigorous exposition of classical conformal symmetry in n dimensions and its quantization in two dimensions. The conformal groups are determined and the appearence of the Virasoro algebra in the context of the quantization of two-dimensional conformal symmetry is explained via the classification of central extensions of Lie algebras and groups. Part II surveys 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.

Zielgruppe

Research

Autoren/Hrsg.

Schottenloher, Martin

Inhaltsverzeichnis

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 Towards Conformal Field Theory.- Representation Theory of the Virasoro Algebra.- Projective Representations of Diff+ ( ) and More.- String Theory as a Conformal Field Theory.- Foundations of Two-Dimensional Conformal Quantum Field Theory.- Mathematical Aspects of the Verlinde Formula.