Lie Groups, Lie Algebras, Cohomology and some Applications in Physics

A self-contained introduction to the cohomology theory of Lie groups and some of its applications in physics.

Josi A. de Azcárraga (Author), Josi M. Izquierdo (Author)

9780521597005, Cambridge University Press

Paperback, published 6 August 1998

476 pages, 22 b/w illus.
24.7 x 17.5 x 2.5 cm, 0.785 kg

'The material presented is essentially self-contained and at a basic graduate text level. The material is also well organized and the book reads very well … The book is warmly recommended.' Classical and Quantum Gravity

Now in paperback, this book provides a self-contained introduction to the cohomology theory of Lie groups and algebras and to some of its applications in physics. No previous knowledge of the mathematical theory is assumed beyond some notions of Cartan calculus and differential geometry (which are nevertheless reviewed in the book in detail). The examples, of current interest, are intended to clarify certain mathematical aspects and to show their usefulness in physical problems. The topics treated include the differential geometry of Lie groups, fibre bundles and connections, characteristic classes, index theorems, monopoles, instantons, extensions of Lie groups and algebras, some applications in supersymmetry, Chevalley-Eilenberg approach to Lie algebra cohomology, symplectic cohomology, jet-bundle approach to variational principles in mechanics, Wess-Zumino-Witten terms, infinite Lie algebras, the cohomological descent in mechanics and in gauge theories and anomalies. This book will be of interest to graduate students and researchers in theoretical physics and applied mathematics.

Preface
1. Lie groups, fibre bundles and Cartan calculus
2. Connections and characteristic classes
3. A first look at cohomology of groups and related topics
4. An introduction to abstract group extension theory
5. Cohomology groups of a group G and extensions by an abelian kernel
6. Cohomology of Lie algebras
7. Group extensions by non-abelian kernels
8. Cohomology and Wess–Zumino terms: an introduction
9. Infinite-dimensional Lie groups and algebras
10. Gauge anomalies
List of symbols
References
Index.

Subject Areas: Physics [PH]