Modern gauge theory started with Yang and Mills's proposal about isotopic gauge invariance of the strong interactions. The Yang–Mills theory, a non- Abelian gauge theory, emerged totally within the framework of the quantum field programme, in which interactions are transmitted by field quanta and realized through localized coupling between field quanta. Physically, it obtained impetus from the charge independence of the strong nuclear forces, but at the same time was constrained by the short-range character of the same forces. Methodologically, it was driven by the desire of having a universal principle to fix a unique form of couplings among many possibilities. Physicists took some interest in the Yang–Mills theory, in part because they thought it renormalizable, but soon abandoned it because there seemed no way to have a gauge-invariant mechanism to account for the short-range character of the nuclear forces. (Chapter 9)

The difficulty was overcome, first in the early 1960s, by the discovery of the spontaneous breakdown of symmetry (section 10.1), and then in the early 1970s by the discovery of asymptotic freedom (section 10.2). With the proof, by Veltman and 't Hooft, of the renormalizability of non-Abelian gauge theories (section 10.3), a seemingly self-consistent conceptual framework was available to the particle physics community.

Conceptually, the framework is very powerful in describing various fundamental interactions in nature, and in exploring novel, global features of field theories that were supposed to be local, which features have direct bearings on our understanding of the structure of the vacuum and the quantization of charges (section 10.4).