Group Theory and Its Applications in Physics

1. Front Matter

   Pages I-XV

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2. Symmetry and the Role of Group Theory

   • Teturo Inui, Yukito Tanabe, Yositaka Onodera

   Pages 1-6

3. Groups

   • Teturo Inui, Yukito Tanabe, Yositaka Onodera

   Pages 7-29

4. Vector Spaces

   • Teturo Inui, Yukito Tanabe, Yositaka Onodera

   Pages 30-43

5. Representations of a Group I

   • Teturo Inui, Yukito Tanabe, Yositaka Onodera

   Pages 44-81

6. Representations of a Group II

   • Teturo Inui, Yukito Tanabe, Yositaka Onodera

   Pages 82-101

7. Group Representations in Quantum Mechanics

   • Teturo Inui, Yukito Tanabe, Yositaka Onodera

   Pages 102-114

8. The Rotation Group

   • Teturo Inui, Yukito Tanabe, Yositaka Onodera

   Pages 115-168

9. Point Groups

   • Teturo Inui, Yukito Tanabe, Yositaka Onodera

   Pages 169-182

10. Electronic States of Molecules

    • Teturo Inui, Yukito Tanabe, Yositaka Onodera

    Pages 183-219

11. Molecular Vibrations

    • Teturo Inui, Yukito Tanabe, Yositaka Onodera

    Pages 220-233

12. Space Groups

    • Teturo Inui, Yukito Tanabe, Yositaka Onodera

    Pages 234-258

13. Electronic States in Crystals

    • Teturo Inui, Yukito Tanabe, Yositaka Onodera

    Pages 259-290

14. Time Reversal and Nonunitary Groups

    • Teturo Inui, Yukito Tanabe, Yositaka Onodera

    Pages 291-315

15. Landau’s Theory of Phase Transitions

    • Teturo Inui, Yukito Tanabe, Yositaka Onodera

    Pages 316-332

16. The Symmetric Group

    • Teturo Inui, Yukito Tanabe, Yositaka Onodera

    Pages 333-359

17. Back Matter

    Pages 360-397

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This book has been written to introduce readers to group theory and its ap­ plications in atomic physics, molecular physics, and solid-state physics. The first Japanese edition was published in 1976. The present English edi­ tion has been translated by the authors from the revised and enlarged edition of 1980. In translation, slight modifications have been made in. Chaps. 8 and 14 to update and condense the contents, together with some minor additions and improvements throughout the volume. The authors cordially thank Professor J. L. Birman and Professor M. Car­ dona, who encouraged them to prepare the English translation. Tokyo, January 1990 T. Inui . Y. Tanabe Y. Onodera Preface to the Japanese Edition As the title shows, this book has been prepared as a textbook to introduce readers to the applications of group theory in several fields of physics. Group theory is, in a nutshell, the mathematics of symmetry. It has three main areas of application in modern physics. The first originates from early studies of crystal morphology and constitutes a framework for classical crystal physics. The analysis of the symmetry of tensors representing macroscopic physical properties (such as elastic constants) belongs to this category. The sec­ ond area was enunciated by E. Wigner (1926) as a powerful means of handling quantum-mechanical problems and was first applied in this sense to the analysis of atomic spectra. Soon, H.

• Group theory
• Mathematical Physics
• phase transition
• quantum physics
• solid-state physics
• spectra

• Japan Women’s University, Bunkyo-ku, Tokyo 112, Japan

  Teturo Inui, Yukito Tanabe

• Department of Physics, School of Science and Technology, Meiji University, Tama-ku, Kawasaki 214, Japan

  Yositaka Onodera

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