From Covariant Rotation Geometry to Yang-Mills Theory: A Relational Ontology Approach to Fundamental Interactions

This paper demonstrates that Yang-Mills theory, the mathematical foundation of the Standard Model, can be derived from the first principles of a relational ontology as described by Covariant Rotation Geometry (CRG). We begin by elevating CRG from its original Abelian formulation to a general non-Abelian framework capable of describing finite rotations. By introducing dynamics, we show that the requirement of relational consistency naturally gives rise to a non-Abelian gauge field, whose curvature measures the failure of relational transitivity. We then establish that the only gauge-invariant and Lorentz-invariant action describing the dynamics of this relational structure is the Yang-Mills action. This result suggests that Yang-Mills theory is not an ad-hoc mathematical construct but the inevitable consequence of a physical reality built upon relational principles. Our work provides a new conceptual foundation for gauge theories, unifying the geometric intuition of Einstein with the symmetry principles of Yang.