A new generation of books on group theory for physicists has appeared over the last ten years . Many of them deal only with elementary particle physics or with condensed matter physics . This volume by Prof. Jin-Quan Chen is a serious attempt to cover a broad range of applications of group theory to physics. It begins with an introduction to the elements of group theory and the theory of representations . Representations of finite groups and character theory are carefully treated and applied in later chapters to point groups and space groups, where thorough and practical information is given about molecular and crystal groups.The permutation group is discussed in detail, and its use in finding the irreps of unitary groups is carefully and completely covered. Lie groups and Lie algebras are treated sufficiently to enable their use in elementary particle physics, with a thorough presentation of Dynkin diagrams and the reduction of products.For spectroscopy and, in particular , nuclear spectroscopy, this is the first up-to-date and thorough treatment of the calculation of isoscalar factors and coefficients of fractional parentage. There are extensive tables and indications of computational methods. With his collaborators in Nanjing and Philadelphia, Chen has contributed extensively to new developments over the past decade . These researches are incorporated into the present book, of which a preliminary version was published a few years ago in the People's Republic of China.It has been a pleasure for me to talk with Chen many times about group theory and a special pleasure to welcome the appearance of this book.
Morton Hamermesh
PrefaceConscious of the frustration we experienced as we tried to learn group theory, and apply it to problems in physics , F. Wang , M. J. Gao and I endeavoured in 1974 to carry out a systematic reform of traditional group representation theory . Our aim was to establish a new approach to group representations in accordance with the concept and method used in quantum mechanics, so that it would be much more accessible to physicists and chemists. Mr. Pei-tying Wang typed the initial draft of Chapters 4-9, and my son, Bing-Qing wrote several software codes for facilitating the typing and proof-reading of the manuscript . Without their help it would be inconceivable that the re-writing could have been accomplished within half a year.Special mention must be made of Professors B. Bayman, M. Hamermesh and K.T. Hecht for their constant interest and many illuminating discussions, and D . H. Feng , who gave me the opportunity and encouragement to teach a course on group theory at Drexel University.Last but not least I would like to thank Professors
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