03093 - Lie Groups, Physics, and Geometry - An Introduction for Physicists, Engineers and Chemists [Gilmore].pdf

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LIE GROUPS, PHYSICS, AND GEOMETRY

An Introduction for Physicists, Engineers and Chemists

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 relation of Lie groups with many branches of

mathematics and physics, and illustrates these with concrete computations. Many

examples of Lie groups and Lie algebras are given throughout the text, with appli-

cations of the material to physical sciences and applied mathematics. The relation

between Lie group theory and algorithms for solving ordinary differential equa-

tions 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.

Robert Gilmore

is a Professor in the Department of Physics at Drexel Univer-

sity, 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.

LIE GROUPS,

PHYSICS, AND GEOMETRY

An Introduction for Physicists, Engineers

and Chemists

ROBERT GILMORE

Drexel University, Philadelphia