The problems start with the title, of course. The author actually knows this, since the preface begins “This book is the English edition of the Japanese book *Group Representations for Quantum Theory*…”

And it only gets worse:

The original Japanese book covers several topics in representation theory, that is related to quantum theory.

This book conducts lecture courses on mathematics for physicists.

And after explaining that there are six topics essential to the application of representation theory to quantum physics,

Unfortunately, although there are so many good mathematical books for a part of six topics, no book contains all of these topics because they are too segmentalized. Further, some of them are written in an abstract way in mathematics style and, often, the materials are too segmented. At least, the notation is not familiar to people working on quantum theory.

Those are from the first page of the preface, but there is a lot of this in the text as well:

However, a Hermitian matrix may be a degenerate… (p. 3)

Since possible unitary representation and possible projective unitary representations are limited to a small class due to the property of the group of interest, the transformation with respect to the given quantum system derives various restrictions for the states of the quantum system. (p. 38)

Next, we discuss the same discussion as the above… (p. 272)

Open the book at random and you will find a mangled sentence of some kind. In most cases, one can guess the intended meaning, but we are often left wondering exactly what is meant. In a textbook intended for beginners, this is deadly: even a little bit of imprecision can lead to serious mathematical errors.

*None* of this, of course, is the author’s fault. Prof. Hayashi is not a native English speaker, and since he teaches at Nagoya University in Japan, probably does not get to listen to English speakers very often. The question, then, is why a publisher would so betray one of their authors. All it would have taken is one careful reading by a competent copyeditor.

Fernando Q. Gouvêa is Carter Professor of Mathematics at Colby College.