YangMills theory describes non-Abelian gauge theories from "summary" of The Quantum Theory of Fields by Steven Weinberg,Weinberg S
Yang-Mills theory is a quantum field theory that describes interactions between elementary particles through non-Abelian gauge symmetries. In this framework, the fundamental fields are associated with vector potentials that transform under a non-Abelian Lie group, such as SU(2) or SU(3). The gauge symmetry of the theory implies that the Lagrangian remains invariant under local transformations of these fields, corresponding to different choices of gauge. The key feature of Yang-Mills theory is the presence of gauge bosons, which mediate the interactions between particles. These gauge bosons arise from the kinetic terms in the Lagrangian, which involve the covariant derivatives of the vector potentials. The non-Abelian nature of the theory leads to self-interactions among the gauge bosons, giving rise to non-trivial dynamics and rich phenomenology. One of the central results of Yang-Mills theory is the existence of massless gauge bosons, which are associated with the unbroken gauge symmetries of the theory. These massless particles play a crucial role in the fundamental forces of nature, such as the electromagnetic, weak, and strong interactions. The non-Abelian nature of the gauge symmetries also leads to the phenomenon of asymptotic freedom, where the strength of the interactions decreases at high energies. In summary, Yang-Mills theory provides a powerful framework for describing the fundamental forces of nature in terms of non-Abelian gauge symmetries. The theory predicts the existence of massless gauge bosons and allows for self-interactions among these particles. It has been successfully applied to the electromagnetic and strong interactions, as well as the unified electroweak theory. Yang-Mills theory stands as a cornerstone of modern theoretical physics, with far-reaching implications for our understanding of the universe.
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