Gauge theory

Summary

A gauge theory is a field theory whose action does not change under local symmetry transformations, chosen independently at each point of spacetime. In geometric terms, its basic field is a connection on a principal bundle, and its symmetry group is the gauge group of that bundle. Electromagnetism is the gauge theory of the circle group $U(1)$, and the Standard Model of particle physics is a gauge theory with group $SU(3) \times SU(2) \times U(1)$. In mathematics, gauge theory gave the Yang–Mills equations, instantons and new invariants of four-manifolds.