A Mathematical Introduction to Conformal Field Theory

  • M. Schottenloher

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

Table of contents

  1. Front Matter
    Pages I-3
  2. Mathematical Preliminaries

    1. Front Matter
      Pages 5-6
    2. M. Schottenloher
      Pages 23-38
    3. M. Schottenloher
      Pages 39-62
    4. M. Schottenloher
      Pages 75-85
  3. First Steps Toward Conformal Field Theory

    1. Front Matter
      Pages 87-89
    2. M. Schottenloher
      Pages 91-102
    3. M. Schottenloher
      Pages 103-120
    4. M. Schottenloher
      Pages 121-152
    5. M. Schottenloher
      Pages 171-212
    6. M. Schottenloher
      Pages 213-233
    7. M. Schottenloher
      Pages 235-237
  4. Back Matter
    Pages 239-249

About this book


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

Authors and affiliations

  • M. Schottenloher
    • 1
  1. 1.Ludwig-Maximilians-Universitä München80333 MünchenGermany

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