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How did Yang and Mills use Lie groups to study the strong interaction?

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differential geometry An annular strip (the region between two concentric circles) can be cut and bent into a helical strake that follows approximately the contour of a cylinder. Techniques of differential geometry are employed to find the dimensions of the annular strip that will best match the required curvature of the strake.

In 1954, physicists Chen Ning Yang and Robert L. Mills developed a gauge theory that utilized Lie groups to describe subatomic interactions. By applying the mathematical framework of Lie groups—which possess specific symmetry and continuity properties—they sought to formulate a gauge-invariant theory for the strong interaction.123

Specifically, Yang and Mills used the group of gauge transformations to address the isospin of strongly interacting particles. Their work established a geometric structure where the physics of a quantum field remains unchanged under these group transformations. This approach was later foundational for quantum chromodynamics, which describes the strong force through the exchange of gluons. Unlike electromagnetism, the Yang-Mills framework allows force-carrier particles to interact with one another, a property that helps explain the confinement of quarks and the short-range nature of the strong force.214