# A Mathematical Introduction to Conformal Field Theory

Part of the Lecture Notes in Physics book series (LNP, volume 759)

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Part of the Lecture Notes in Physics book series (LNP, volume 759)

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.

algebra conformal field theory verlinde formula vertex algebra virasoro algebra

- DOI https://doi.org/10.1007/978-3-540-68628-6
- Copyright Information Springer-Verlag Berlin Heidelberg 2008
- Publisher Name Springer, Berlin, Heidelberg
- eBook Packages Physics and Astronomy
- Print ISBN 978-3-540-68625-5
- Online ISBN 978-3-540-68628-6
- Series Print ISSN 0075-8450
- Buy this book on publisher's site