Although published in 1983, this book predates the discoveries made at CERN of the intermediate vector bosons. This discovery coupled with the discovery of weak neutral currents more than a decade before, solidified the role of gauge theories in providing a unified theory of elementary particle interactions. The author does a fine job of introducing the history of gauge theory, and also its conceptual foundations, emphasizing the physics, and not the mathematical formalism. In the book, the Einstein theory of gravitation is explained, naturally, as the first successful gauge theory, the local coordinates of which can be defined as the gravitational field. This, the author explains, movtivated H. Weyl to generalize this to one of the other forces of nature, namely electromagnetism. Weyl needed a quantity that would transform like the electromagnetic potential under changes of position. For this he chose to assert that the norm of a physical vector should depend on position (i.e. a change of "scale"), and thus to compare lengths at different places in space-time one needs a connection. This connection did transform like a vector potential and thus gave Weyl what he needed. His theory was rejected however by Einstein and Bergmann, and many others. The soundest of their objections was based on an argument from quantum theory, namely that a natural scale involving the particle's wavelength is characteristic of the quantum theory, and the wavelength is dependent on mass, which cannot depend on position. The author also overviews the role of gauge invariance in the Hamilton-Jacobi formulation of electromagnetic theory. The inclusion of this discussion is rare in books and articles written on gauge theory at the time of this one (or before), but it does serve to motivate nicely the place that gauge invariance holds in the quantum theory of electromagnetism. In this context, the Aharonov-Bohm effect is discussed, and asserted to be proven experimentally. This is a controversial assertion however, and the one can say without any mental reservations that after a thorough study of the literature on the experiments studying this effect, that they are inconclusive as of this date. In addition, the author discusses the reasons that gauge invariance took so long to be accepted by the physical community. In the quantum realm, one of these reasons, he argues, is due to the fact that gauge transformations were related to the phase of the wavefunction, and not to coordinates in space-time. The latter geometric view was thus missing from the concept of gauge invariance in quantum physics. In addition, the gauge group did not seem to play a role in the dynamics of the quantum theory, it merely being a sort of ancillary property that had no predictive power. Such beliefs ended of course with the rise of Yang-Mills theories, but the road to acceptance of Yang-Mills gauge theories was not a smooth one. It took many years before the non-renormalizability of these theories was worked out. In the meantime, mathematicians were becoming more attracted to the study of gauge theories, and the formulation of gauge theories from a mathematically rigorous point of view was gaining major advances, excluding the path integral quantization of these theories, which to this date, has defied a mathematically rigorous treatment. The author details well the development of gauge theories from the paper of Yang-Mills, up until the time of the book's publication. The Weinberg-Salam theory and its triumph in the prediction of neutral currents is oultined, and a brief introduction is given to quantum chromodynamics, the gauge theory of the strong interaction. The Weinberg-Salam theory was further solidified in the early eighties due to the experimental evidence for intermediate vector bosons. That gauge theores are successful in predicting elementary particle phenomena has now become a cliche. There is still of course an enormous amount of work to be done, particularly from the standpoint of the calculation of quantities in low-energy strong-interaction physics, and the prediction of bound states using quantum gauge field theories. Superstring and M-theories have supplanted a lot of the research in gauge theories, this research also involving the mathematical community to a large degree. Indeed, Weyl, Einstein, Yang, and Mills would no doubt be astonished at the level of mathematics now being used in these theories. The mathematical constructions used in their theories was considered esoteric at the time, but it pales in comparison to the dizzying heights that mathematics has been taking in superstring and M-theories. These developments are very exciting and one can probably say with a fair degree of confidence that the role of gauge theory will remain in research in high energy physics in the 21st century. |