Mathematicians, beware! This book is not for you!! The tiny amount of fibre bundle mathematics in this book is entirely from th... Read More

Mathematicians, beware! This book is not for you!! The tiny amount of fibre bundle mathematics in this book is entirely from the physicist's point of view. Connections are defined here as Lie-algebra-valued forms on the space-time manifold, not as connection forms on the principal bundle as mathematicians do it. (If you want the mathematical framework, see Bleecker's Gauge Theory and Variational Principles.)The strongest point of this book is that it motivates many aspects of gauge theory by explaining which parts of the subject arose in each stage of the progressive historical development of particle physics. The author assumes that the reader has a good background in quantum electrodynamics, and also a fair background in superconductivity theory. If you have a good understanding of fibre bundles, that won't help you at all....This book by Keihachiro Moriyasu (1940-1992), who was an experimental physicist (as far as I can tell from information on the internet), presents the historical development of gauge theory concepts for particle physics, showing how the theoretical ideas were modified and extended from the time of classical EM gauge invariance (which was already known in 1870) up to 1983. Unfortunately the W and Z bosons were verified experimentally only in 1983, apparently a few months after this book was written. But the predictions of masses and other properties explained in this book were verified by experiment.The author begins the story with Weyl's general-relativity-based gauge theory, which is really only important because it explains the confusing name of the subject. It should really be called phase-curvature-field theory, or something like that, because what is now called gauge theory involves connection forms on principal bundles with compact structure groups, which are more like bundles of phases, nothing to do with scaling groups.Then the author progresses through the various stages of the historical development, including especially the 1954 Yang-Mills theory, which did not get very much approbation at first because they required zero rest-mass, the technical difficulties of breaking gauge symmetry to introduce non-zero mass (the 1961-1964 spontaneous symmetry breaking developments), the 1967/68 Weinberg-Salam theory, and applications of Y-M theory to (non-quantum) chromodynamics. Regrettably the W and Z boson experimental verification occurred just a little bit too late to be included in this book.All in all, it's a valuable little 177-page book which helps to make sense of the big heavy gauge theory books which you can buy now. One minor fault is the use of footnotes for all references, which is great for a 10-page research paper, but not so great for a 177-page book. The other minor fault is that the author did not seem to understand the fibre bundle point of view at all. The mathematics in this book is very weak, particularly in the first 14 pages. Luckily I persevered, because at page 22, when the author starts explaining physics, there are many valuable insights which I have not seen in other presentations of gauge theory. I have put exclamation marks in the margin at very numerous points in this book. For example, on page 26, the author explains why SU(2) is the group chosen for isotopic-spin in Y-M theory. It seems totally obvious when it is explained properly! (Mathematicians need such explanations. Probably physicists don't.) Read Less