Geometric Unification of Gravity and Gauge Interactions from Rotational Two-Form Geometry

AbstractWe develop a unified geometric field-theoretic framework, Quaternion AngularMomentum Gravity (QAMG), based on the principle of minimal geometric completeness. In this approach, rotational and angular-momentum degrees of freedomare promoted to fundamental geometric variables, encoded by an antisymmetrictwo–form field valued in an internal fiber space, together with an independentangular–momentum curvature sector and a global angular–momentum neutrality(GAN) constraint that fixes the vacuum structure.Starting from a single unified action, we derive a closed and self-consistentsystem of field equations, including a generalized Einstein equation for the spacetime metric, a dynamical equation for the two–form rotational geometry, a unifiedYang–Mills–type equation for internal gauge connections, and a global constraintequation enforcing GAN. All interaction sectors arise from the same variational principle, without introducing fundamental scalar fields or ad hoc symmetry-breakingpotentials.A central result is that gauge interactions emerge as geometric phases of theunified structure. Phase comparability of fiber-valued two–form fields inevitablyleads to internal connections and curvature, and hence to non-Abelian gauge structure. In the infrared limit, integrating out heavy two–form fluctuations inducesstandard Yang–Mills kinetic terms. Electromagnetic, weak, and strong interactionsare realized as different algebraic projections of the same unified gauge geometry. Inparticular, strong interactions emerge as a robust geometric consequence, whereasweak interactions appear conditionally, depending on the GAN-allowed vacuumbranch and the effective mass scale of the two–form sector.Wefurther demonstrate that QAMG admits well-defined correspondence limits.In the absence of rotational flux, the theory reduces exactly to general relativity.In the Abelian limit, the unified gauge sector reproduces Maxwell electrodynamics,while SU(2) and SU(3) projections recover the weak and strong gauge dynamics, respectively. We verify that there exist non-empty regions of parameter spacein which GAN constraints, infrared and ultraviolet stability, and induced gaugedynamics are simultaneously satisfied, establishing the realizability of the unifiedgeometric structure.These results show that QAMG provides a coherent and geometrically transparent framework for unifying gravitation and gauge interactions, compatible withestablished low-energy physics while offering a controlled setting for exploring extensions beyond the standard model.