Atlas of Fundamental Concepts

The geometric language starts with smooth manifolds, Lie groups, fiber bundles, and principal bundles. A principal connection defines parallel transport and covariant differentiation; its curvature is the geometric counterpart of field strength. The physical branch identifies gauge fields with local connection data and develops Abelian and non-Abelian Yang–Mills theories, culminating in QED, QCD, electroweak theory, and the Standard Model gauge group.