The first part of this book gives a detailed, self-contained and mathematically rigorous exposition of classical conformal symmetry in n dimensions and itsquantization in two dimensions. In particular, 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. The second part presents several different approaches to conformal field theory and surveys more advanced topics, such as the representation theory of the Virasoro algebra, conformalsymmetry within string theory, an axiomatic approach to Euclidean conformallycovariant quantum field theory and a mathematical interpretation of the Verlinde formula in the context of moduli spaces of holomorphic vector bundles on aRiemann surface. INDICE: Conformal Transformations and Conformal Killing Fields.- The Conformal Group.- Central Extensions of Groups.- Central Extensions of Lie Algebrasand Bargmann's Theorem.- The Virasoro Algebra.- 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: Some Further Developments. References.- Index.
- ISBN: 978-3-540-68625-5
- Editorial: Springer
- Encuadernacion: Cartoné
- Páginas: 310
- Fecha Publicación: 01/08/2008
- Nº Volúmenes: 1
- Idioma: Inglés