Condensed matter field theory

Condensed matter field theory 

A Altland and B Simons 

Cambridge, UK: Cambridge University Press  | 2006 | 624 pp | ?45.00 (HB) |  ISBN 0521845084 

Reviewed by Dennis Rouvray

Whenever we wish to explore or predict the properties of matter we are obliged to make use of models that yield approximations to reality. Although the reliability of our models has improved out of all recognition over the past half century, they still cannot provide us with exact answers. Moreover, the type of model we adopt depends very much on the nature and amount of the matter being investigated. 

Thus, microscopic amounts of matter in the form of individual atoms or comparatively small molecules are best described in terms of the Schr?dinger equation or the relativistically correct Dirac equation. By contrast, the study of macroscopic matter, which typically consists of a mole or more of material, is usually based on statistical techniques, such as those of statistical mechanics.  

But what about samples of matter that lie between these two extremes? How are we to treat what are usually referred to as mesoscopic systems? That the problem has become an urgent one is evidenced by the many experimental advances and breakthroughs of recent years in areas such as nanotechnology, high-temperature superconductors, ultracold atomic gases and conducting polymers. 

Condensed matter field theory  has been written with the express purpose of presenting the response of the theoreticians to this challenge. The book is a comprehensive reference work on the methods that have been developed to characterise mesoscopic systems. Most of these methods are highly mathematical because dealing with mesoscopic systems is in general far more difficult than modelling either molecular or bulk matter.  

Nevertheless, this work is so well written that it succeeds in making even the most intricate and abstruse models admirably clear. Moreover, it is timely in that it brings the reader completely up to date on most of the newer approaches currently in vogue, including those that make resort to topological principles. This high-level book is eminently suitable for researchers in the field, although it could also be read with interest by advanced students because the numerous info sections elucidate and expand upon the many themes addressed. It seems likely that this very attractive book will remain a standard reference work in its field for years to come.