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Classical theory of gauge fields. Translated by Steven S. Wilson. (English) Zbl 1036.81002

Princeton, NJ: Princeton University Press (ISBN 0-691-05927-6/hbk). x, 444 p. (2002).
Traditionally, gauge theory is considered part of quantum field theory and the platform on which modern particle physics is built on, though some of its concepts can perfectly be understood already at a classical level. Rubakov’s book focuses on the classical aspects. It is based on a lecture course at the Moscow State University and organized so that 10 out of 17 chapters do not even require a rudimentary knowledge of quantum mechanics and hence lacks motivation right from the start. The puzzled student might ask: what is the purpose of classical fields with no physical reality behind except for the case of classical electrodynamics? Will he be motivated if he is treated to an abundance of mathematical constructions with the particle concept missing? Will his reaction be other than confusion when he encounters the term Goldstone bosons in Chapter 5.2 referring to a massless scalar field with no Bose statistics behind? Rubakov concedes that quantum theory is needed to physically interpret the Dirac equation (in Chapter 14). But miraculously he gets around second quantization and Fermi statistics avoiding Hilbert spaces and the concept of a vacuum state. Fermions become simply synonymous with Dirac fields.
It seems to me that Rubakov looked for a shortcut to the Standard Model of present-day particle physics without having to spend too much time (in fact no time at all) on the intricacies of operator field theory. It is hard to envisage the student benefitting from an exposition with no prospect of understanding the field-particle relation.

MSC:

81-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to quantum theory
81Txx Quantum field theory; related classical field theories
70S20 More general nonquantum field theories in mechanics of particles and systems
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