Yang-Mills Theory

Yang-Mills theory is a framework in theoretical physics, developed by Chen-Ning Yang and Robert Mills in 1954, that extends the gauge invariance underlying Maxwell's electromagnetism to more general, non-Abelian symmetry groups. Where electromagnetism's gauge symmetry allows only a single kind of charge, Yang-Mills fields carry their own charge under the symmetry group itself, letting the force-carrying particles interact with one another the way photons cannot. The original 1954 paper met with little immediate interest, since the theory as written seemed to require massless force carriers nowhere observed in nature. That obstacle was resolved in the 1960s and 1970s through the Higgs mechanism and asymptotic freedom, and Yang-Mills theory became the mathematical foundation of the Standard Model, underlying both the strong nuclear force and the electroweak theory unifying electromagnetism with the weak interaction. The Clay Mathematics Institute lists the existence and mass gap of Yang-Mills theory among its seven Millennium Prize Problems.