Ma, Zhong-Qi Group theory for physicists. (English) Zbl 1157.20001 Hackensack, NJ: World Scientific (ISBN 978-981-277-141-4/hbk; 978-981-277-142-1/pbk). xx, 491 p. (2007). In my review of the monograph “Group Theory” by P. Cvitanović [Group theory. Birdtracks, Lie’s, and exceptional groups. Princeton: Princeton University Press (2008; Zbl 1152.22001)], it is written that with the coming new year, it is getting harder and harder to create a new book on group theory. This year witnesses at least two such books. The other is the one under review. Despite that the two books are about group theory, they are substantially different, in the purposes, in the presentations, and correspondingly, in the readers’ audiences. Ma’s monograph is designed as a lecture course in group theory for graduate students in physics and theoretical chemistry. It is composed of ten chapters which are partly, as has to be anticipated, similar by the contents to the analogous lecture courses. Chapter 1 briefly reviews the necessary tools of linear algebra. Chapters 2 and 3 provide the fundamental core of Ma’s book. Chapter 2 presents the fundamental definitions of the theory of groups, among which are the definitions of a group, subgroup, cosets, invariant subgroup, and the direct product of two groups. And Chapter 3 is introductory to the representations of groups. The next two Chapters, 4 and 5, are largely applied: 4 deals with the three-dimensional rotation group and 5 with crystallographic groups. The next few steps upward to more fundamental group theory stuff, the author makes in the remainder of his book. These include groups of permutations, Lie groups and Lie algebras, unitary groups, real orthogonal and symplectic groups. Each chapter is supplied with a big variety of home-kind exercises. Reviewer: Eugene Kryachko (Liège) Cited in 2 ReviewsCited in 11 Documents MSC: 20-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to group theory 00A06 Mathematics for nonmathematicians (engineering, social sciences, etc.) 22-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to topological groups 17-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to nonassociative rings and algebras 81-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to quantum theory 20Bxx Permutation groups 20Cxx Representation theory of groups 22Exx Lie groups 81V55 Molecular physics 20C35 Applications of group representations to physics and other areas of science 22E70 Applications of Lie groups to the sciences; explicit representations 20H15 Other geometric groups, including crystallographic groups Keywords:group theory; symmetries; subgroups; cosets; polyhedra; homomorphisms; point groups; irreducible representations; Schur theorem; characters; Clebsch-Gordan coefficients; idempotents; rotation groups; Lie groups; Lie algebras; Euler angles; momentum operators; N-body quantum systems; centers of mass; crystallographic groups; permutation groups; Young tableaux; Littlewood-Richardson rule; Cartan matrices; Dynkin diagrams; Killing forms; Chevalley bases; mass formulas; mesons; baryons; wave functions; unitary groups; orthogonal groups; tensor representations; spinor representations; Lorentz group; symplectic groups Citations:Zbl 1152.22001 PDFBibTeX XMLCite \textit{Z.-Q. Ma}, Group theory for physicists. Hackensack, NJ: World Scientific (2007; Zbl 1157.20001)