Differential Geometry and Lie Groups for Physicists 1st Edition by Marián Fecko ISBN 0521187966 978-0521187961

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Product details: 

ISBN 10:0521187966 

ISBN 13:978-0521187961

Author:Marián Fecko

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.

Table of contents: 

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

Poincaré 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

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Tags: Marián Fecko, Differential, Geometry