This book provides an introduction to the cohomology theory of Lie groups and Lie algebras and to some of its applications in physics. The mathematical topics covered include the differential geometry of Lie groups, fibre bundles and connections, characteristic classes, index theorems, extensions of Lie groups and algebras, Chevalley - Eilenberg cohomology of Lie algebras, symplectic cohomology and an introduction to infinite-dimensional Lie groups and algebras. The physical applications include the U 1 Dirac monopole, SU 2 instantons and various aspects of anomalies Wess - Zumino - Witten terms, Abelian and non-Abelian anomaly, path-integral derivation and descent equations.
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.
Lie Groups and Lie Algebras: A Physicist's Perspective
The book would be most useful for graduate students and researchers in theoretical and mathematical physics who are interested in applications of Lie group and Lie algebra cohomology in particle physics. Even though most of the proofs of the mathematical theorems are presented, the focus is more on explaining the ideas than striving for mathematical rigour, therefore the book would be less suitable for those students who are interested in the mathematical foundations per se. Since the book seems to aim for physics students, it is a pity that - apart from the topic of anomalies which is covered very thoroughly - the applications are only briefly touched upon.
Other applications of current interest, such as non-Abelian monopoles and instantons for gauge groups other than SU 2 as well as their moduli spaces, are not discussed at all even though the necessary mathematical background is presented and thus they seem well within the scope of the book. It must be said, however, that the lack of different applications is compensated for by an excellent set of bibliographical notes and references at the end of each chapter.
ISBN 13: 9789814603270
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Viewed times. Anonymous Anonymous 31 4 4 bronze badges. I think it is quite elementary and you might like it. He also has two more books, about semi-Riemannian Geometry and Black Holes might as well learn a bit of GR in the way. I'll keep these suggestions as comments, since I'm no expert in Lie theory, and am in fact looking for references too.
PSI / - Lie Groups and Lie Algebra (Dupuis) | Perimeter Institute
I have the strong feeling that a physicist looking for some basic familiarity can get by without the tangent space definition of the Lie algebra. About group theory, so far I haven't seen the need for anything too sophisticated e. Sylow theory, solvable groups, etc.
The first chapter of the first text I linked may be enough background for the rest of it. LB1 LB1 56 3 3 bronze badges. Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password.
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