Non-Abelian Yang-Mills theory defines a gauge-invariant action constructed from the trace of the square of the field strength tensor derived from non-commuting covariant derivatives, resulting in self-interacting dynamics distinct from Abelian theories like electromagnetism. The core mechanism involves the equations of motion requiring the vanishing of the gauge-covariant divergence of the field strength tensor ($D_{\mu}F^{\mu\nu}_a = 0$), where the nonlinear terms arising from structure constants prevent a linear superposition of fields and invalidate classical solutions as accurate representations of quantum physical states. This framework generalizes the principles of fiber bundle geometry found in General Relativity (Riemann tensor) to describe strong interactions via Quantum Chromodynamics, establishing that massless gluon degrees of freedom inherently lead to confinement rather than observable long-range color forces at low energies.
Non-Abelian Yang-Mills theory defines a gauge-invariant action constructed from the trace of the square of the field strength tensor derived from non-commuting covariant derivatives, resulting in sel…