Gauge fields

Abstract

This article is a survey of the history and ideas of gauge theory. Described here are the gradual emergence of symmetry as a driving force in the shaping of physical theory; the elevation of Noether’s theorem, relating symmetries to conservation laws, to a fundamental principle of nature; and the force of the idea (‘‘the gauge principle’’) that the symmetries of nature, like the interactions themselves, should be local in character. The fundamental role of gauge fields in mediating the interactions of physics springs from Noether’s theorem and the gauge principle in a remarkably clean and elegant way, leaving, however, some tantalizing loose ends that might prove to be the clue to a future deeper level of understanding. The example of the electromagnetic field as the prototype gauge theory is discussed in some detail and serves as the basis for examining the similarities and differences that emerge in generalizing to non-Abelian gauge theories. The article concludes with a brief examination of the dream of total unification—all the forces of nature in a single unified gauge theory, with the differences among the forces due to the specific way in which the fundamental symmetries are broken in the local environment.