Lie Groups, Lie Algebras, Cohomology and some Applications in Physics
$112.00 (C)
Part of Cambridge Monographs on Mathematical Physics
 Authors:
 Josi A. de Azcárraga, Universitat de València, Spain
 Josi M. Izquierdo, Universitat de València, Spain
 Date Published: September 1998
 availability: Available
 format: Paperback
 isbn: 9780521597005
$
112.00
(C)
Paperback
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Now in paperback, this book provides a selfcontained 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, fiber bundles and connections, characteristic classes, index theorems, monopoles, instantons, extensions of Lie groups and algebras, some applications in supersymmetry, ChevalleyEilenberg approach to Lie algebra cohomology, symplectic cohomology, jetbundle approach to variational principles in mechanics, WessZuminoWitten 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.
Read more Selfcontained introduction to important area in theoretical physics
 Suitable for both researchers and advanced graduate students
 In highly respected series
 Includes list of symbols and detailed references
Reviews & endorsements
'[This book] reserves for itself a special place among other presentations by successfully trying to be selfcontained. Its strong point is a systematic exposition of the mathematical background in an accessible form … the book is most useful for physicists who want to go beyond the standard physics review type introduction to differential geometry. The book offers them a quite rigorous but at the same time lucid and selfcontained presentation.' Mathematical Reviews
See more reviews'This book is a useful contribution to the constantly growing literature that is devoted to the mathematicsphysics interface …The book is a welcome relief to the physicist searching for a physically motivated yet mathematically rigorous and systematic exposition of gauge anomalies … The book under review reserves itself a special place among other presentations by successfully trying to be selfcontained. Its strong point is a systematic exposition of the mathematical background in an accessible form … a quite rigorous but at the same time lucid and selfcontained presentation.' Mathematical Reviews
'The material presented is essentially selfcontained 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
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×Product details
 Date Published: September 1998
 format: Paperback
 isbn: 9780521597005
 length: 476 pages
 dimensions: 244 x 170 x 24 mm
 weight: 0.75kg
 contains: 22 b/w illus.
 availability: Available
Table of Contents
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 nonabelian kernels
8. Cohomology and Wess–Zumino terms: an introduction
9. Infinitedimensional Lie groups and algebras
10. Gauge anomalies
List of symbols
References
Index.
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