Gauge Fields and Yang–Mills Unification from Information Geometry

We extend the Information Geometry Unification Principle (IGUP) to incorporate gauge symmetries and Yang–Mills theory. By introducing principal fiber bundles over the quantum information manifold, we identify gauge potentials as affine connections and field strengths as bundle curvatures. The Yang–Mills Lagrangian arises naturally as the curvature scalar of the internal symmetry bundle. We unify electromagnetism, the electroweak interaction, and quantum chromodynamics within the information geometric framework, demonstrating that all fundamental forces are manifestations of information geometry. This work completes the unification of gravity, quantum theory, thermodynamics, and the Standard Model.