A Mathematical Introduction to Conformal Field Theory
Based on a Series of Lectures given at the Mathematisches Institut der Universität Hamburg
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Beschreibung
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 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 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.
This book is an important text for researchers and graduate students.
Part I gives a detailed, self-contained and mathematically rigorous exposition of classical conformal symmetry in n dimensions and its quantization in two dimensions. 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. Part II surveys 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.
Autor*in
Martin Schottenloher
Themen in »A Mathematical Introduction to Conformal Field Theory«
Konforme Feldtheorie Konforme Gruppe Modulraum stabiler Vektorbündel Verlinde-Formel Virasoro-Algebra conformal field theory conformal groups moduli spaces of holormorphic vector bundles quantum field theory string theory verlinde formula virasoro algebra