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The Dawning of Gauge Theory LOCHLAINN O'RAIFEARTAIGH, 1997 Princeton, NJ, Princeton University Press ix + 249 pp., $US 69.50 (hardback), SUS 29.95 (paperback) ISBN 0-691-02978-4 (hardback), 0-691-02977-6 (paperback)
Lochlainn O'Raifeartaigh is one of the leading experts on group theory and its application to the modern gauge theories of elementary particle physics. His latest book deals with the emergence of the gauge principle, which is currently thought to govern all of the four fundamental interactions of physics. O'Raifeartaigh says that the discovery of the gauge principle as a fundamental theory of physics was a slow and tortuous process that took more than 60 years-an evolution rather than a revolution. During the course of this evolution, gauge invariance developed from an incidental symmetry of electromagnetism to a general principle underlying all of the fundamental interactions of particle physics.
O'Raifeartaigh's book is divided into two parts. Part I deals with the period from 1918 to 1929. It covers the origins of gauge theory as a geometric principle and its reinterpretation, after the birth of quantum mechanics, as a framework for describing both gravitational and electromagnetic interactions. Part II of the book deals with the period from 1938 to 1956, and it covers attempts to generalize gauge theory to include nuclear interactions as well.
Gauge theory originated as an effort by Hermann Weyl in 1918 to generalize Einstein's theory of gravitation to include both gravitation and electromagnetism. Weyl was trying to extend the locality of space-time to a different kind of infinitesimal geometry, in which it would be possible to choose the scale of measurement at each point in space at will. His plan was to relate electromagnetism to this new kind of invariance, just as Einstein had connected gravitation with invariance under general continuous transformations of space-time coordinates. Weyl's point was that standard Riemannian geometry was slightly defective, because, although it appeared to be infinitesimal, it contained a residue of rigid Euclidean geometry in that it maintained that the magnitudes of vectors, in contrast to their directions, are path-independent with respect to parallel transfer. This is why Weyl's theory was named gauge theory. The term gauge was appropriate, since the rescaling of the metric tensor due to the path factor could be interpreted as a change of length...