A Mathematical Introduction to Conformal Field Theory : Based on a Series of Lectures given at the Mathematisches Institut der Universität Hamburg / by Martin Schottenloher.

Format:

Book

Author/Creator:

Schottenloher, Martin, 1944- author.

Contributor:

Universität Hamburg. Mathematisches Seminar.

Series:

Lecture Notes in Physics Monographs ; 43

Language:

English

Subjects (All):

Quantum theory.

Spintronics.

Quantum Physics.

Local Subjects:

Quantum Physics.

Spintronics.

Physical Description:

1 online resource (VIII, 144 p.)

Edition:

1st ed. 1997.

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1997.

Language Note:

English

Summary:

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.

Contents:

Mathematical Preliminaries

Conformal Transformations and Conformal Killing Fields

The Conformal Group

Central Extensions of Groups

Central Extensions of Lie Algebras and Bargmann’s Theorem

The Virasoro Algebra

First Steps Towards Conformal Field Theory

Representation Theory of the Virasoro Algebra

Projective Representations of Diff+ ( ) and More

String Theory as a Conformal Field Theory

Foundations of Two-Dimensional Conformal Quantum Field Theory

Mathematical Aspects of the Verlinde Formula.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references and index.

ISBN:

3-540-70690-9