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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.

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

Citations:

Zbl 1152.22001
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