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.

Synopsis

This textbook presents an introduction to group theory and its applications in atomic, molecular and solid-state physics. It provides the background on the mathematical theory of groups and then shows why group theory is a powerful tool for solving physics problems. Worked examples and exercises with hints and answers encourage self-study, and the inclusion of some advanced material, such as the theory of induced representations and ray representations, Racah theory of atomic spectra, and Laudau theory of second-order phase transitions, should interest professionals in the field.

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