The Method of Moments in Electromagnetics, by W.C. Gibson

are the renormalisation-group fixed points, parametrised by a small number of relevant perturbations. Under the action of the renormalisation group any low-energy theory ‘flows’ to the vicinity of the highenergy fixed point in whose basin of attraction it lies. The application of the semi-classical approximation to the functional integral around a Gaussian fixed point of the renormalisation group provides evidence of nonperturbative effects in the field theory, such as solitons and instantons. An instanton is defined as a stable, finite-action solution of the Euclidean field equations of a d-dimensional quantum field theory. Such a solution can also be viewed as a static solution of the same theory in d þ 1 dimensions, i.e. as a soliton of the higher-dimensional theory. Banks discusses several examples, including the Yang–Mills instantons and the ’t Hooft–Polyakov magnetic monopoles. So, does he succeed in emulating Mandl? Only partially, I think. First, in the pursuit of brevity, he has deliberately excluded supersymmetry and finite (i.e. non-zero) temperature field theory, so a full coverage of the developments since Mandl’s text is ruled out from the start. But in any case I doubt that a novice could really get to grips with, say, the quantisation of the Standard Model of particle physics, and its experimental predictions, using just this text, even with the prerequisites specified by Banks. As he emphasises, completing the Problems is an essential part of the course, and I think that these would probably compel the student to turn to more discursive treatments, such as Peskin and Schroeder. On the other hand, the insights and overviews provided by Banks, particularly on the renormalisation group, are much harder to come by in competing texts. I am not convinced that it is possible to do a latter-day Mandl. There is much to admire in this attempt, so if it is a defeat, it is an extremely honourable one.