YangMillsteorier
Yang-Mills theories are a class of gauge theories based on non-abelian Lie groups that describe how elementary particles interact through gauge bosons. In these theories, the gauge fields A_μ^a act as connections on a principal G-bundle, and the dynamics are governed by the field strength F_μν^a = ∂_μ A_ν^a − ∂_ν A_μ^a + g f^{abc} A_μ^b A_ν^c. The covariant derivative D_μ = ∂_μ − i g A_μ^a T^a encodes local invariance under the Lie group G. The non-abelian structure implies that gauge bosons carry charge and interact with each other, producing self-interaction terms in the Lagrangian.
Historically, Yang-Mills theory was introduced in 1954 by Chen-Ning Yang and Robert Mills as a non-abelian generalization
Key properties of Yang-Mills theories include renormalizability and, for non-abelian groups, asymptotic freedom—the coupling becomes weaker
Applications are wide, spanning calculations in the Standard Model and non-perturbative studies with lattice gauge theory.