by V Gribov and J Nyiri, 2001 Cambridge University Press (Cambridge monographs on particle physics, nuclear physics and cosmology no. 13), ISBN 0521662281, £55/$80.
This short book is based on the lectures of Vladimir Gribov that were given in Leningrad in 1974. It was completed, after his death in 1997, by his collaborator Julia Nyiri and it provides a pleasant introduction to the basics of field theory and quantum electrodynamics (QED). One of the book’s strengths is its intuitive and relatively leisurely introduction to quantum field theory (QFT) via the Feynman propagator and diagram approach that is particularly suited to students on their first approach to the forbidding machinery of modern QFT. Indeed, in its treatment of elementary but fundamental topics – such as the construction of the scattering amplitude; the relation between causality, unitarity and analyticity in the Mandelstam plane; and tree-level processes such as the Compton effect or soft electron bremsstrahlung – it can be compared to two of the best older texts on quantum electrodynamics – Feynman’s own book of this title and the volume on QED of the Landau and Lifshitz series. Unfortunately it also inherits deficiencies from its origins in the early 1970s.
Though the last two chapters discuss radiative corrections in QED and some aspects of renormalization theory, such as Ward identities, no mention is made of the central topic of the renormalization group, either in its older Gell-Mann-Low form or in the more modern Wilsonian guise within the effective field theory picture. Thus there are no anomalous dimensions of operators or running couplings as encapsulated in beta-functions – apart from what the student may find rather confusing remarks on the “zero charge problem”. Without these crucial tools a student is ill-prepared to explore the deeper properties of quantum field theory.
In addition there is no discussion of spontaneous symmetry breaking, the Higgs mechanism, Yang-Mills theory, ghosts, dimensional regularization, anomalies, or the operator product expansion. Therefore none of the physics of the theory of the strong or weak interactions can be discussed. So sadly, despite its pleasing and pedagogical introduction to the basics of QED, it can’t compete with modern quantum field theory texts, such as Peskin’s “Introduction to Quantum Field Theory”, as a full introductory course. However, I can recommend it as an enjoyable basic supplement to more complete texts.
