M. Schottenloher (auth.)3540686258, 9783540686255
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.
Table of contents :
Front Matter….Pages I-3
Front Matter….Pages 5-6
Conformal Transformations and Conformal Killing Fields….Pages 7-21
The Conformal Group….Pages 23-38
Central Extensions of Groups….Pages 39-62
Central Extensions of Lie Algebras and Bargmann’s Theorem….Pages 63-73
The Virasoro Algebra….Pages 75-85
Front Matter….Pages 87-89
Representation Theory of the Virasoro Algebra….Pages 91-102
String Theory as a Conformal Field Theory….Pages 103-120
Axioms of Relativistic Quantum Field Theory….Pages 121-152
Foundations of Two-Dimensional Conformal Quantum Field Theory….Pages 153-170
Vertex Algebras….Pages 171-212
Mathematical Aspects of the Verlinde Formula….Pages 213-233
Appendix A….Pages 235-237
Back Matter….Pages 239-249
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