I. S. Zheludev

Pp. 224. Berlin: Akademie Verlag, 1990
Price £10.00. ISBN 3-05-500688-7

This book is a German translation of a Russian text originally published in 1987. It provides an interpretation of some of the phenomena of crystal physics in terms of symmetry.

The opening chapters give a very full account of symmetry groups, including those not normally discussed in textbooks on the subject. Thus, for example, the sphere with mirror planes is discussed separately from that in which those elements have been removed, and the rotating cylinder and cone are similarly distinguished from their stationary counterparts.

There follows a treatment of scalars, vectors and tensors that concentrates particularly on their relationships with the point groups.

A chapter on the symmetry of space and time includes a brief account of the symmetry theory of elementary particles as well as a discussion of the relative motions of galaxies in terms of space-like and time-like intervals. These highly theoretical topics of modern physics may seem out of place in a book bearing such a title as this one, but they serve to underline the thesis that all phenomena determined by conditions of symmetry are dependent on invariance with respect to the inversion of time. The stability of elementary particles is further discussed in an Appendix.

The book goes on to consider phase transitions in crystals. The symmetry relations that determine these are discussed in detail, as are the phenomena of pyroelectricity and piezoelectricity. Finally, some aspects of the optical properties of crystals form the subject of a separate section.

Throughout the book, the treatment is very theoretical and relies greatly upon fundamental considerations. The point is made strongly that natural phenomena can occur only if symmetry relationships permit them, but that not all changes so allowed will necessarily happen in practice. The exposition is clear, and the book should be useful to those wishing to gain an insight into this fascinating subject.

M. Kapel

Procter Department
University of Leeds
Leeds LS2 9JT
England