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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.
List of contents
| Preface | |
| Acknowledgments | |
| Introduction | 3 |
| 1 | Gauge Transformations in Classical Electromagnetism | 13 |
| Gravitation and Electricity | 24 |
| 2 | Aftermath of Einstein's Gravitational Theory | 38 |
| 3 | Generalizations of Einstein's Theory | 44 |
| On the Unification Problem of Physics | 53 |
| Quantum Theory and Five-Dimensional Relativity | 59 |
| On the Invariant Form of the Wave and Motion Equations for a Charged Point-Mass | 70 |
| 4 | The Renaissance of Weyl's Idea: EM Gauge Theory | 77 |
| On a Remarkable Property of the Quantum-Orbits of a Single Electron | 87 |
| Quantization as an Eigenvalue Problem | 91 |
| Quantum-Mechanical Interpretation of Weyl's Theory | 94 |
| 5 | Weyl's Classic, 1929 | 107 |
| Electron and Gravitation | 121 |
| 6 | Klein's Serendipity, 1938 | 147 |
| On the Theory of Charged Fields | 152 |
| 7 | Pauli's Dimensional Reduction, 1953 | 166 |
| Meson-Nucleon Interaction and Differential Geometry | 171 |
| 8 | The Yang-Mills Theory, 1953-54 | 182 |
| Isotopic Spin Conservation and a Generalized Gauge Invariance | 185 |
| Conservation of Isotopic Spin and Isotopic Gauge Invariance | 186 |
| 9 | Shaw's SO(2) Approach, 1954-55 | 197 |
| Invariance under General Isotopic Spin Transformations | 200 |
| 10 | Utiyama's General Approach, 1954-55 | 208 |
| Invariant Theoretical Interpretation of Interaction | 213 |
| Conclusion | 240 |
| References | 243 |
| Index | 247 |
About the author
Lochlainn O'Raifeartaigh
Summary
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.
Additional text
"The book thus performs a double service: it offers a rewarding description of the development of the gauge symmetry idea that
is complete even without the original papers, and it makes those original papers readily accessible to physicists and mathematicians. . . . This book represents an important contribution to the history of fundamental ideas in physics."
