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.

Duality in Yang’s theory of gravity

“…The historical route to the SU (2) gauge theory is beautifully laid out by Mills [3], with several ramifications [4] mainly due to the paper of Schrödinger [5], in which the compact 'Clifform' formula [6] for the Riemannian curvature anticipated the concept of gauge curvature, see also the letter of the late Bob Mills to one of the authors reprinted in Appendix A, we thank his widow, Elise Mills, for her kind permission to publish this letter. 1 Here we will concentrate on the gravitational aspect: In 1974 Yang [2] considered the possible replacement of Einstein's general relativity (GR) by an affine gauge theory with a Yang-Mills type action.…”

Magnetic field generation from self-consistent collective neutrino-plasma interactions

“…In Section IV, the nonlinear neutrino-plasma fluid equations and the Maxwell equations for the electromagnetic field are derived. Through the Noether method [34][35][36], an exact energy-momentum conservation law is also derived and the process of energy-momentum transfer from the neutrinos to the electromagnetic field and the plasma is discussed. In Section V, magnetic-field generation, magnetic-helicity production and magnetic equilibrium involving neutrino-plasma interactions are investigated.…”

A gauge symmetric band model of the Woodward–Hoffmann rules

“…The interrelationship of symmetry, conservation, and gauge invariance (through gauge fields) has been discussed in physics and mathematics for some time [30]. Weyl' s work shows how to use the idea of gauge invariance as a dynamical principle [31].…”