Yang–Mills theory

Summary

Yang–Mills theory is the gauge theory whose action is the Yang–Mills functional, the integral of the squared norm of the curvature of a connection. For the circle group it is Maxwell's theory of light. For a non-abelian group such as $SU(2)$ or $SU(3)$ the gauge fields interact with each other. Chen-Ning Yang and Robert Mills introduced the non-abelian theory in 1954. Quantum Yang–Mills theories describe the strong and weak forces, and giving a rigorous construction of them is a Millennium Prize Problem.