Description 
1 online resource (xv, 249 pages) : illustrations 
Series 
Lecture notes in physics ; 759 

Lecture notes in physics ; 759.

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 Toward Conformal Field Theory  Representation Theory of the Virasoro Algebra  String Theory as a Conformal Field Theory  Axioms of Relativistic Quantum Field Theory  Foundations of TwoDimensional Conformal Quantum Field Theory  Vertex Algebras  Mathematical Aspects of the Verlinde Formula  Appendix A 
Summary 
The first part of this book gives a detailed, selfcontained 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 twodimensional 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 selfcontained 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 
Bibliography 
Includes bibliographical references and index 
Notes 
English 

Print version record 
Subject 
Quantum field theory.


Conformal invariants.


Physique.


Conformal invariants.


Quantum field theory.

Form 
Electronic book

ISBN 
9783540686286 

3540686282 

9783540686255 

3540686258 
