Robert Gilmore

Lie Groups, Physics, and Geometry (eBook, ePUB)

An Introduction for Physicists, Engineers and Chemists

• Format: ePub

Produktbeschreibung

Describing many of the most important aspects of Lie group theory, this book presents the subject in a 'hands on' way. Rather than concentrating on theorems and proofs, the book shows the applications of the material to physical sciences and applied mathematics. Many examples of Lie groups and Lie algebras are given throughout the text. The relation between Lie group theory and algorithms for solving ordinary differential equations is presented and shown to be analogous to the relation between Galois groups and algorithms for solving polynomial equations. Other chapters are devoted to differential geometry, relativity, electrodynamics, and the hydrogen atom. Problems are given at the end of each chapter so readers can monitor their understanding of the materials. This is a fascinating introduction to Lie groups for graduate and undergraduate students in physics, mathematics and electrical engineering, as well as researchers in these fields.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 17. Januar 2008
• Englisch
• ISBN-13: 9781139637688
• Artikelnr.: 52941270

Autorenporträt

Robert Gilmore is a Professor in the Department of Physics at Drexel University, Philadelphia. He is a Fellow of the American Physical Society, and a Member of the Standing Committee for the International Colloquium on Group Theoretical Methods in Physics. His research areas include group theory, catastrophe theory, atomic and nuclear physics, singularity theory, and chaos.

Inhaltsangabe

1. Introduction
2. Lie groups
3. Matrix groups
4. Lie algebras
5. Matrix algebras
6. Operator algebras
7. Exponentiation
8. Structure theory for Lie algebras
9. Structure theory for simple Lie algebras
10. Root spaces and Dykin diagrams
11. Real forms
12. Riemannian symmetric spaces
13. Contraction
14. Hydrogenic atoms
15. Maxwell's equations
16. Lie groups and differential equations
References
Index.