Differential Geometry and Lie Groups for Physicists
Differential Geometry and Lie Groups for Physicists by Marián Fecko, published by Cambridge University Press on October 12, 2006, is a comprehensive textbook that introduces essential geometrical concepts relevant to theoretical physics and applied mathematics. Spanning 714 pages, this edition is designed to provide a solid foundation in topics such as manifolds, tensor fields, and symplectic geometry, making it a valuable resource for advanced undergraduate and graduate students.
Readers will find that the book emphasizes understanding through practical engagement, featuring over 1000 exercises with complete solutions or detailed hints. The informal writing style aims to facilitate learning, preparing students for further studies in areas like Lagrangian mechanics, electromagnetism, and relativity. With a focus on mathematical and computational principles, this textbook serves as an effective guide for both coursework and self-study, requiring only a standard introductory background in mathematics.
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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.
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