The condensed matter view of QM

This is a graduate text written by a condensed-matter physicist and not a particle or atomic physicist. The main aim is to achieve an understanding of how relativistic effects are included in electronic structure calculations and concomitant experiments (such as Faraday and Kerr rotations), an area where the author is a leading international expert. The book is very readable and could easily be used as background reading to an advanced relativistic quantum mechanics undergraduate course as well as the postgraduate audience for which it is intended. Despite the author's beliefs, this book is not very mathematical, although it does suffer from some heavy algebra which could be justified by the use of the book as a source of reference for the details of numerical relativistic calculations.

The first half of the book is a standard account of Klein-Gordon and Dirac equations, combined with physical interpretations for their pathologies. The atomic problem and a few additional exact solutions are then covered which will be of much interest to a student of condensed matter. Once this material has been dealt with, the book departs from the norm and enters the realm of relativistic electronic structure calculations. This second half is quite unique and will prove valuable to the small group of scientists who research in this area. The simple physical pictures of how relativity distorts and corrupts Fermi surfaces are very instructive and should be read and appreciated by all condensed-matter physicists.

If you are putting on a course on advanced quantum mechanics, then consider this book for background reading and assistance with the physical concepts. Any researcher desiring to pursue a career in relativistic condensed matter will find it invaluable.

Martin Long is senior lecturer in physics, University of Birmingham.