On symmetry - by physicists for physicists

This book is part of a graduate student series in physics written by physicists for physicists, but it is a didactic text despite its mathematical appearance. The authors have gone out of their way to give it a personal bias and give extensive referencing. As the central topic is symmetry, angular momentum features at length and the book has much overlap with older texts, such as Alan Edmonds (1957) and Morris Rose (1957), and with later texts on quantum mechanics. It retains a character all of its own, reflecting the painstaking approach of the authors. The refactorisation of Clesbch Gordan coefficients is typical. My only regret is that they assume knowledge of Legendre polynomials. They have even given precise connections with earlier notations. There are gems of excursions into speciality interests, which could be inspiring to keen graduate students.

This book will amply reward graduate students learning the trade of symmetries, and indeed, more experienced researchers. My pleasure at reading full treatments of active versus passive views of transformations (much neglected in general) was heightened by the sections on tensor operators and the Wigner Eckart theorem, which revealed great depth of understanding of how apparently similar symbols and formulae often carry curiously different meanings in their correct interpretation. Certain sections of this book will admirably extend good undergraduates too. I hope it is widely read.

K. J. Barnes is professor of theoretical physics, University of Southampton.