Differential Geometry and Lie Groups for Physicists

Name: Differential Geometry and Lie Groups for Physicists
Price: 170.14 USD
Availability: InStock
ISBN: 9780521845076

ISBN-10: 0521845076

ISBN-13: 9780521845076

Edition: 2006

Authors: Mariï¿½n Fecko

List price: $176.00

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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…

Book details

List price: $176.00
Copyright year: 2006
Publisher: Cambridge University Press
Publication date: 10/12/2006
Binding: Hardcover
Pages: 714
Size: 6.93" wide x 9.96" long x 1.54" tall
Weight: 3.388
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



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


Appendices


Bibliography


Index