The Dawning of Gauge Theory

During the course of this century, gauge invariance has slowly emerged from being an incidental symmetry of electromagnetism to being a fundamental geometrical principle underlying the four known fundamental physical interactions. The development has been in two stages. In the first stage (1916-1956) the geometrical significance of gauge-invariance gradually came to be appreciated and the original abelian gauge-invariance of electromagnetism was generalized to non-abelian gauge invariance. In the second stage (1960-1975) it was found that, contrary to first appearances, the non-abelian gauge-theories provided exactly the framework that was needed to describe the nuclear interactions (both weak and strong) and thus provided a universal framework for describing all known fundamental interactions. In this work, Lochlainn O'Raifeartaigh describes the former phase.

O'Raifeartaigh first illustrates how gravitational theory and quantum mechanics played crucial roles in the reassessment of gauge theory as a geometric principle and as a framework for describing both electromagnetism and gravitation. He then describes how the abelian electromagnetic gauge-theory was generalized to its present non-abelian form. The development is illustrated by including a selection of relevant articles, many of them appearing here for the first time in English, notably by Weyl, Schrodinger, Klein, and London in the pre-war years, and by Pauli, Shaw, Yang-Mills, and Utiyama after the war. The articles illustrate that the reassessment of gauge-theory, due in a large measure to Weyl, constituted a major philosophical as well as technical advance.

The author has written additional papers on the history of gauge theory,which can easily be found via an online search, and this book could be considered an excellent introduction to them. He addresses more modern developments in gauge theories as they relate to the early history, such as superstring theory. Readers who study this book, will not only come away with a deeper appreciation of the underlying concepts in gauge theory, but will be prepared to appreciate in greater detail these modern developments, being as they are the best current hope for understanding the nonperturbative region in quantum field theories and string theories.


Thought provoking!   June 26, 2002
 4 out of 4 found this review helpful

I picked this book up when it first came out and gave it a quick read. Now, five years later, having just read it again, I cannot believe that it was not as indelible in my mind then as it is now. A combination of original papers, peppered with O'Raifeartaigh's informed remarks and hindsight, produces an eligant book that follows a timeline that begins with the greatest minds in physics of the last century. The fits and starts of physicists such as London, Fock, Schrodinger, and Klein, though viewed as disparate attempts at the time, give way to an understanding of analogous formulations, and the suggestion of something powerful and underlying. This, of course, being gauge invariance, has equipped the modern physicist with tools that has produced the most striking conclusions: QED and electroweak theory to name a few. The way in which these notions arose, I suspect, is not common knowledge. Just as understanding a breakthrough may only require the reading of a few seminal papers by a few people, the foundation of a good theory often is the result of many people and many false starts. O'Raifeartaigh uses excellent judgement in what to include, and what not to, in his book. It does, incidentally, start with Kuluza-Klein, and run all the way though the 50's to Yang and Mills theory of isotopic spin and gauge invariance (conservation).

A knowledge of tensor analysis (the index (i.e., f_i,j) type), group theory, and differetial geometry is assumed. Topology would broaden the experience.


The papers speak for themselves   March 25, 1998
 11 out of 11 found this review helpful

A powerhouse collection of papers in modern Physics! O'Raifeartaigh's introduction and commentary brings each paper's contribution into sharp focus (with benefit of hindsight, of course).

The papers by Weyl and Kaluza are startling in their simplicity and boldness. If you haven't read them yet, these two alone justify buying the book.

The book does assume familiarity with General Realitivity and tensor analysis. I would highly reccomend Lawden's "An Intoduction to Tensor Calculus, Relativity and Cosmology", or Misner's very complete "Gravitation".