Lie Groups Lie Algebras Cohomology and Some Applications in Physics

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 fiber 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.