This book is the tale of 80 years of quest for a unified theory of the physical world. Although this goal is not yet achieved, an important discovery has been made, i.e., all the four fundamental interactions (gravitational, weak and strong nuclear forces) are governed by the so-called gauge principle. This principle determines, up to some constant parameters, the interactions of the mesons (those which are mediating the above mentioned interactions) with themselves and with non-radiative matter.
According to the author, the discovery of the gauge principle may be separated into three distinct stages. In the first stage H. Weyl [Berl. Ber., 465-480 (1918; JFM 46.1300.01)]that gauge invariance corresponds to the conservation of electric charge in the same way that coordinate-invariance corresponds to the conservation of energy and momentum in gravitation. But the attempt by Weyl, and shortly after by Th. Kaluza [Berl. Ber., 966-972 (1921; JFM 48.1032.03, JFM 48.1327.01)]to unify electromagnetism and gravitation ignored the existence of the other two fundamental forces, namely, the weak and strong nuclear forces. Thus, in the second stage of the development of the theory, the gauge invariance used in electromagnetism was generalized to a form that could be used for the nuclear interactions. The first attempt in this direction is due to Klein in 1938 who assumed that the mesons mediating the nuclear interactions were vectors like the photon. This stage of the theory culminated in the theory of Yang and Mills. Guided by the desire to make the isotopic spin symmetry of the strong interactions local, they invented the SU(2) gauge theory. The basic idea of this theory was that the isospin symmetry of the strong interactions should be gauged in the same way as the electromagnetic phase symmetry. The third stage consisted in the recognition of gauge theory as a reliable theory of nuclear interactions. A number of new concepts like parity violation, spontaneous symmetry breaking, color symmetry, asymptotic freedom, etc., were introduced at that time.
The present book focusses on the first two stages, which are less known because during these stages the gauge theory was a slow and torturous process whose development was by far less significant than that of gravitation and quantum theory. Because the papers on gauge theory were written in German, the author presents the most relevant ones in English translation in this book.
The book comprises two main parts. The development of gauge theory from the foundation laid by Einstein’s theory of gravitation to Weyl’s paper on the relationship between General Relativity and Dirac Electron Theory, is presented in Part I of the book. The papers included in this part are the seminal works of Weyl in 1918 and 1929, and those of Klein, Kaluza, Fock, Schrödinger, and London in the intervening period. The second part treats the generalization of Weyl’s gauge formalism of electromagnetism to non-abelian gauge-theory and contains the articles of Yang and Mills, Klein, Pauli, Shaw and Utiyama.
The hope of the author is that this book will provide a valuable description of how modern gauge theory developed in its early stages.