The first part of this book gives a detailed selfcontained and mathematicallyrigorous exposition of classical conformal symmetry in n dimensions and itsquantiza... » 

The first part of this book gives a detailed selfcontained and mathematicallyrigorous exposition of classical conformal symmetry in n dimensions and itsquantization in two dimensions. In particular the conformal groups aredetermined and the appearance of the Virasoro algebra in the context of thequantization of twodimensional conformal symmetry is explained via theclassification of central extensions of Lie algebras and groups. The secondpart presents several different approaches to conformal field theory andsurveys more advanced topics such as the representation theory of the Virasoroalgebra conformal symmetry within string theory an axiomatic approach toEuclidean conformally covariant quantum field theory and a mathematicalinterpretation of the Verlinde formula in the context of moduli spaces ofholomorphic vector bundles on a Riemann surface. The substantially revised andenlarged second edition makes in particular the second part of the book moreselfcontained and tutorial with many more examples given. Furthermore twonew chapters on Wightmans axioms for quantum field theory and vertex algebrasbroaden the survey of advanced topics. An outlook making the connection withrecent developments has also been added. TOCConformal Transformations andConformal Killing Fields. The Conformal Group. Central Extensions of Groups.Central Extensions of Lie Algebras and Bargmanns Theorem. The VirasoroAlgebra. Representation Theory of the Virasoro Algebra. String Theory as aConformal Field Theory. Axioms of Relativistic Quantum Field Theory.Foundations of TwoDimensional Conformal Quantum Field Theory. VertexAlgebras. Mathematical Aspects of the Verlinde Formula. Appendix SomeFurther Developments. References. Index. «