Lie Groups, Physics, and Geometry: An Introduction for Physicists, Engineers and Chemists

by Robert Gilmore

Overview

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.

Product Details

ISBN-13:	9780521884006
Publisher:	Cambridge University Press
Publication date:	01/17/2008
Edition description:	New Edition
Pages:	332
Product dimensions:	7.24(w) x 9.84(h) x 0.83(d)

About the Author

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.

Table of Contents

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.

What People are Saying About This

From the Publisher

"Gilmore (physics, Drexel U.) takes an applications-base approach to Lie group theory as it relates to certain branches of applied mathematics and the physical sciences, basically distilling what he considers the most useful material of his much longer book </Lie Groups, Lie Algebras, and Some of Their Applications/> (New York: Wiley, 1974). He begins with a discussion of Lie group theory's intellectual underpinnings in Galois theory and concludes with a chapter on the application of Lie group theory to solving differential equations, both subjects that are relatively rare in texts on Lie group theory. In between he offers chapters on matrix groups, Lie algebras, matrix algebras, operator algebras, EXPonentiation, structure theory for Lie algebras, root spaces and Dynkin diagrams, real forms, Riemannian symmetric spaces, contraction, hydrogenic atoms, and Maxwell's equations."
Book News Inc.

"Gilmore is successful in creating a direct and applied approach to the study of Lie Groups."
E. Kincanon, Gonzaga University for CHOICE

"...lively and stimulating exposition. The numerous and varied exercises are a particular strength of the book and lead the motivated reader to explore the diverse connections of Lie groups with a wide range of modern physics. All in all, Lie Groups, Physics, and Geometry is a worthy addition to the literature..."
Peter J. Olver, Physics Today

"This is a great how-to book, where one can find detailed examples worked out completely, covering many and interesting aspects and applications of group theory."
Julio Guerrero, Mathematical Reviews

Editorial Reviews

"Gilmore (physics, Drexel U.) takes an applications-base approach to Lie group theory as it relates to certain branches of applied mathematics and the physical sciences, basically distilling what he considers the most useful material of his much longer book Lie Groups, Lie Algebras, and Some of Their Applications (New York: Wiley, 1974). He begins with a discussion of Lie group theory's intellectual underpinnings in Galois theory and concludes with a chapter on the application of Lie group theory to solving differential equations, both subjects that are relatively rare in texts on Lie group theory. In between he offers chapters on matrix groups, Lie algebras, matrix algebras, operator algebras, EXPonentiation, structure theory for Lie algebras, root spaces and Dynkin diagrams, real forms, Riemannian symmetric spaces, contraction, hydrogenic atoms, and Maxwell's equations."
Book News Inc.

"Gilmore is successful in creating a direct and applied approach to the study of Lie Groups."
E. Kincanon, Gonzaga University for CHOICE

"...lively and stimulating exposition. The numerous and varied exercises are a particular strength of the book and lead the motivated reader to explore the diverse connections of Lie groups with a wide range of modern physics. All in all, Lie Groups, Physics, and Geometry is a worthy addition to the literature..."
Peter J. Olver, Physics Today

"This is a great how-to book, where one can find detailed examples worked out completely, covering many and interesting aspects and applications of group theory."
Julio Guerrero, Mathematical Reviews

From the Publisher