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Differential Geometry and Lie Groups for Physicists

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ISBN-10: 0521845076

ISBN-13: 9780521845076

Edition: 2006

Authors: Mari�n Fecko

List price: $196.00
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Description:

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.
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Book details

List price: $196.00
Copyright year: 2006
Publisher: Cambridge University Press
Publication date: 10/12/2006
Binding: Hardcover
Pages: 714
Size: 6.75" wide x 10.00" long x 1.50" tall
Weight: 3.432
Language: English

Introduction
The concept of a manifold
Vector and tensor fields
Mappings of tensors induced by mappings of manifolds
Lie derivative
Exterior algebra
Differential calculus of forms
Integral calculus of forms
Particular cases and applications of Stoke's Theorem
Poincar�(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
Appendices
Bibliography
Index