A Mathematical Introduction to Conformal Field Theory. Lecture Notes in Physics, Band 759

Seitenzahl:

252

Gewicht:

524 g

Auflage:

2nd ed.

Erschienen bei:

Springer

Kurzbeschreibung

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 presents several different approaches to conformal field theory and surveys more advanced topics, 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 recent developments has also been added. TOC: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.- Representation Theory of the Virasoro Algebra.- String Theory as a Conformal Field Theory.- Axioms of Relativistic Quantum Field Theory.- Foundations of Two-Dimensional Conformal Quantum Field Theory.- Vertex Algebras.- Mathematical Aspects of the Verlinde Formula.- Appendix: Some Further Developments. References.- Index.

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 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 presents several different approaches to conformal field theory and surveys more advanced topics, 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 recent developments has also been added.

Inhaltsverzeichnis

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.- Representation Theory of the Virasoro Algebra.- String Theory as a Conformal Field Theory.- Axioms of Relativistic Quantum Field Theory.- Foundations of Two-Dimensional Conformal Quantum Field Theory.- Vertex Algebras.- Mathematical Aspects of the Verlinde Formula.- Appendix: Some Further Developments. References.- Index.

Mehr über...

Mehr über:  Feldtheorie (physikalisch), conformal field theory, virasoro algebra, vertex algebra, verlinde formula, Mathematics / Algebra / General, Mathematics / Mathematical Analysis, Science / Mathematical Physics

Mehr von: 

Mehr von:  Martin Schottenloher, Springer-Verlag GmbH