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Quantum field theory. (English) Zbl 0555.46038
Cambridge etc.: Cambridge University Press. XII, 443 p. £40.00; $ 74.50 (1985).
Quantum field theory by Lewis H. Ryder is a very nice pedagogical introduction to the application of this, by now standard instrument, to modern ideas on particle physics. It ranks very honourably in the collection of such books which appeared since the early 80’s. I found it clear, well written, abundantly documented and assigned to help the student to grasp the many facts of this subject. For instance it illustrates many subtleties by physical examples which range from the Bohm Aharonov effect, superconductivity to \(\pi\)-Nucleon scattering solitons, monopoles.... It contains ten chapters and culminates in chapter 9 and 10 on renormalisation and topological objects. Perhaps a minor criticism is that infinities and renormalisation are discussed so late in the book, leaving at first the impression that local quantum field theory is such a straightforward subject. The choice of the path integral formalism is natural as the main guide to construct the various models, \(\phi^ 4\), QED, Yang Mills fields... Of course as the author admits he could not include other recent topics - particularly supersymmetries etc... otherwise the book would have become monstruous.
Each chapter closes with a short summary and well chosen references mostly to reviews, summer school courses... which should help the reader to enrich his study of the subject. There are also numerous very amusing quotes. The one in French for chapter X starts unfortunately with a misprint and does not give the name of the poet (I guess it is Jacques Prevert) showing the decline of the study of foreign languages in English speaking countries - But, remaining serious, the very few misprints that this reader could spot shows the very good job that the author has made as a very valuable and recommendable literature on the subject.
Reviewer: C.Itzykson

46N99 Miscellaneous applications of functional analysis
81T17 Renormalization group methods applied to problems in quantum field theory
81T05 Axiomatic quantum field theory; operator algebras
81T08 Constructive quantum field theory
81-02 Research exposition (monographs, survey articles) pertaining to quantum theory
46-02 Research exposition (monographs, survey articles) pertaining to functional analysis