The Yang–Mills equations are a set of partial differential equations that describe the behavior of gauge fields in the context of gauge theory, which is a fundamental aspect of modern theoretical physics. Named after physicists Chen-Ning Yang and Robert Mills, who formulated them in 1954, these equations generalize Maxwell's equations of electromagnetism to non-Abelian gauge groups, which are groups that do not necessarily commute.
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Stationarity of the Yang-Mills action in the absence of sources gives , using the adjoint gauge covariant derivative. This dynamical equation differs from the geometric gauge-theory Bianchi identity.