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."
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