Many body physics

Quantum theory of the electron liquid 
Gabriele Giuliani and Giovanni Vignale 
Cambridge, UK: Cambridge University Press | 2005 | 798pp | ?50.00 (HB) | ISBN 0521821126 
Reviewed by David Logan 

Modern electronic devices and materials, whether at the nanoscale or bulk levels, derive their often dramatic properties from the intricate behaviour of macroscopically large numbers of electrons (the electron liquid) and the many-body quantum mechanics of this canonical state.  

The area is huge, and the theoretical techniques that underpin it are tough. Yet the pace at which the field has developed in recent years has led to a need for new texts that add topicality to the many classic books in the area. These should bring modern developments to a new generation of researchers without sacrificing the rigour and pedagogical strengths of earlier works.  

In Quantum theory of the electron liquid the authors seek to do just that, with a wide ranging, self-contained and comprehensive treatment of the subject.  

The book starts essentially from scratch, with three chapters on linear response theory following an introduction and an exposition of Hartree-Fock’s classic mean-field approach. This is succeeded by treatments of perturbation theory and Feynman diagrams, density functional theory, and the normal Landau Fermi liquid. The rich peculiarities of one-dimensional systems, Luttinger liquids and the bosonisation of fermions are given a brief chapter. Another chapter deals with the important area of the quantum Hall effects in quasi two-dimensional materials.  

The authors have sought to emphasise physical ideas as much as the development of theoretical techniques, for which many a graduate student/postdoc will be grateful.  

All in all, this is an excellent book with the bonus of a useful selection of exercises to test the reader’s understanding. It is not of course for the faint hearted - books of nearly 800 pages rarely are - and neither is it for those who are theoretically ill prepared for the venture. But for those with stamina, and a zest for getting to the bottom of how nature really operates, study of this book will certainly repay the effort.