Differential Geometry and Lie Groups for Physicists
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Differential geometry plays an increasingly important role in modern theoretical physics and applied mathematics. This textbook gives an introduction to geometrical topics useful in theoretical physics and applied mathematics, covering: manifolds, tensor fields, differential forms, connections, symplectic geometry, actions of Lie groups, bundles, spinors, and so on. Written in an informal style, the author places a strong emphasis on developing the understanding of the general theory through more than 1000 simple exercises, with complete solutions or detailed hints. The book will prepare readers for studying modern treatments of Lagrangian and Hamiltonian mechanics, electromagnetism, gauge fields, relativity and gravitation. Differential Geometry and Lie Groups for Physicists is well suited for courses in physics, mathematics and engineering for advanced undergraduate or graduate students, and can also be used for active self-study. The required mathematical background knowledge does not go beyond the level of standard introductory undergraduate mathematics courses.
List price: $196.00
Copyright year: 2006
Publisher: Cambridge University Press
Publication date: 10/12/2006
Size: 6.75" wide x 10.00" long x 1.50" tall
|The concept of a manifold|
|Vector and tensor fields|
|Mappings of tensors induced by mappings of manifolds|
|Differential calculus of forms|
|Integral calculus of forms|
|Particular cases and applications of Stoke's Theorem|
|Poincarï¿½(c) Lemma and cohomologies|
|Lie Groups - basic facts|
|Differential geometry of Lie Groups|
|Representations of Lie Groups and Lie Algebras|
|Actions of Lie Groups and Lie Algebras on manifolds|
|Hamiltonian mechanics and symplectic manifolds|
|Parallel transport and linear connection on M|
|Field theory and the language of forms|
|Differential geometry on TM and T*M|
|Hamiltonian and Lagrangian equations|
|Linear connection and the frame bundle|
|Connection on a principal G-bundle|
|Gauge theories and connections|
|Spinor fields and Dirac operator|