By N Cabibbo, L Maiani and O Benhar
CRC Press
There is always great excitement among the academic community when a new book by renowned scientists is published. Written by leading experts in particle physics, this book by Luciano Maiani and Omar Benhar, with contributions from the late Nicola Cabibbo, does not disappoint in this regard. Former CERN Director-General Maiani co-proposed the GIM mechanism, which is required to suppress flavour-changing neutral currents at the tree level and assumed the existence of a fourth quark that was discovered in 1974 at SLAC and BNL, while Cabibbo proposed a solution to the puzzle of electroweak decays of strange particles, which was later extended to give rise to the Cabibbo–Kobayashi–Maskawa mixing matrix. Omar Benhar, an INFN research director and professor at the University of Rome “La Sapienza”, is expert in the theory of many-particle systems, the structure of compact stars and electroweak interactions of nuclei.
Their book is the third volume of a series dedicated to relativistic quantum mechanics, gauge theories and electroweak interactions, based on material taught to graduate students at the University of Rome over a period of several decades. Given that gauge theories are the basis of interactions between elementary particles, it is not surprising that there are many books about gauge theories already out there – among the best are those written by Paul Frampton, J R Aitchison and Anthony Hey, Chris Quigg, Ta-Pei Cheng and Ling-Fong Li. One might therefore think that it is hard to add something new to the field, but this book introduces the reader in a concise and elegant manner to a modern account of the fundamentals of renormalisation in quantum field theories and to the concepts underlying gauge theories.
Containing more than 300 pages organised in 20 chapters and several appendices, the book focuses mainly on quantum electrodynamics (QED), which – despite its simplicity and limitations – serves as the mould of a gauge theory and at the same time it has a high predictive power and numerous applications. The first part of this treatise deals with the quantisation of QED via the path-integral method, from basic to advanced concepts, followed by a brief discussion on the renormalisation of QED and some of its applications, such as bremsstrahlung, the Lamb shift, and the electron anomalous magnetic moment. The prediction of the latter is considered one of the great achievements of QED.
In the second part of the book, the authors cover the renormalisation group equations of QED and introduce the quantisation of non-Abelian gauge theories, finishing with a proof of the asymptotic freedom of quantum chromodynamics. Afterwards, the concept of the running coupling constant is used to introduce a few ideas about grand unification. The final chapters are devoted to concepts related to the Standard Model of particle physics, such as the Higgs mechanism and the electroweak corrections to the muon anomalous magnetic moment. Finally, a few useful formulas and calculations are provided in several appendices.
Throughout the book the authors not only present the mathematical framework and cover basic and advanced concepts of the field, but also introduce several physical applications. The most recent discoveries in the field of particle physics are discussed. This is a book targeted at advanced students accustomed to mental challenges. A minor flaw is the lack of problems at the end of the chapters, which would offer students the possibility to apply the acquired knowledge, although the authors do encourage readers to complete a few demonstrations. This text will be very helpful for students and teachers interested in a treatment of the fundamentals of gauge theories via a concise and modern approach in the constantly changing world of particle physics.
