Book Cover
Author Schottenloher, Martin, 1944-

Title A mathematical introduction to conformal field theory / M. Schottenloher
Edition 2nd ed
Published Berlin : Springer, ©2008


Description 1 online resource (xv, 249 pages) : illustrations
Series Lecture notes in physics ; 759
Lecture notes in physics ; 759.
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
Summary 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 the quantization of two-dimensional 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 self-contained 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
Bibliography Includes bibliographical references and index
Notes English
Print version record
Subject Quantum field theory.
Conformal invariants.
Conformal invariants.
Quantum field theory.
Form Electronic book
ISBN 9783540686286