Group Theoretical Methods and Applications to Molecules and Crystals

by Shoon K. Kim

Overview

This book explains the basic aspects of symmetry groups as applied to problems in physics and chemistry using a unique approach developed by the author. This approach includes working out symmetry groups and their representations, eliminating the undue abstract nature of group theoretical methods. The author has systematized the wealth of knowledge on symmetry groups that has accumulated in the century since Fedrov discovered the 230 space groups. He reconstructs space groups, unitary as well as antiunitary, based on the algebraic defining relations of the point groups. This work will be of great interest to graduate students and professionals in solid state physics, chemistry, mathematics, geology and those who are interested in magnetic crystal structures.

Product Details

ISBN-13:	9780521020381
Publisher:	Cambridge University Press
Publication date:	09/29/2005
Edition description:	Revised ed.
Pages:	512
Product dimensions:	6.69(w) x 9.61(h) x 1.02(d)

Table of Contents

Preface; List of symbols; 1. Linear transformations; 2. Theory of matrix transformations; 3. Elements of abstract group theory; 4. Unitary and orthogonal groups; 5. The point groups of finite order; 6. Theory of group representations; 7. Construction of symmetry adapted linear combinations based on the correspondence theorem; 8. Subduced and induced representations; 9. Elements of continuous groups; 10. The representations of the rotation group; 11. Single- and double-valued representations of point groups; 12. Projective representations; 13. 230 space groups; 14. The representations of space groups; 15. The unirreps of the space groups to energy bands and vibrational modes of crystals; 16. Time reversal, antiunitary point groups and their core presentations; 17. Antiunitary space groups and their core presentations; Appendix. Character tables for the crystal point groups; References.

Editorial Reviews

"...beautifully elegant and forceful in pointing out connections that standard methods gloss over...essential reading for serious practitioners of group theory, who will find that their teaching of the subject is enhanced by this deeper look." Choice

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