Group theory and its applications in physics. Transl. by the authors from the Japanese.
The qualities of this book justify the present ``Study edition'', which is a corrected reprint of the previous English 1990 edition (Zbl 0711.20009). The book is clearly written and well suited for developing a familiarity with the applications of group theory in atomic, molecular and solid state physics. It is a good textbook, even if its title suggests more than one finds in the contents. Thus, for example, the applications in high energy physics and in relativity are not treated and the Lorentz and the \(\text{SU}(3)\) groups are missing. One finds the basic group-theoretical notions, a vector-space foundation for group representations and a selection of specific groups like the rotation group and its connection with \(\text{SU}(2)\), the point groups, the space groups and the symmetric groups. All applications needed in a group theory course are treated: electronic wave functions in atoms, molecules and crystals, molecular orbitals, ligand field theory, normal vibrational modes in molecules and crystals and related optical properties involving excitons in molecular crystals, Raman and infrared spectroscopy and the Landau theory of second order phase transitions. The authors go beyond a first level treatment, still keeping to a plain style. The more advanced paragraphs are clearly marked as such and can be skipped in a first reading. Each chapter contains several examples and a number of exercises, more than two hundred (which is a substantial improvement on the previous edition), with answers and hints for about a quarter of them. In conclusion, this book could very well be used to supplement a lecture course in group theory and it should also be of interest for more experienced scientists.
scientific article; zbMATH DE number 877484