The Axial Nature of Relativistic Quantum Interactions

This record contains an early preprint draft of a research paper on the intrinsic magnetic field of fundamental particles. The paper proposes a purely kinematic and rotational reformulation of fundamental interactions, replacing the traditional ontology of conservative vector fields with a framework based exclusively on axial fields. Leveraging the geometric algebra of complexified Euclidean space Cl(4,0) equipped with an imaginary time axis, the study demonstrates how the strictly tangential nature of temporal evolution intrinsically generates these rotational fields. In the electrodynamic domain, the model analytically deduces an intrinsic magnetic field that reproduces the properties of the fermionic magnetic moment. Crucially, its directional quantization into dichotomous spin-up and spin-down states is not introduced as an ad hoc quantum postulate, but emerges spontaneously as an inevitable consequence of the topological orientability of these axial fields. Furthermore, this geometric approach enables the exact derivation of the leading-order anomalous magnetic moment correction (α/2π) without resorting to quantum vacuum fluctuations. Within the resulting effective potential, the fine-structure constant (α) emerges spontaneously to govern spatial equilibrium, intrinsically bounding the field energy and thereby resolving the classical infinite self-energy paradox. This dynamic equilibrium deterministically justifies the hydrogen atom's stability and energy-level quantization by coupling the electron's magnetic dipole with the proton's intrinsic magnetic field. Extending the formalism to gravity, the postulation of an analogous intrinsic gravitomagnetic field yields the exact derivation of fermionic spin (L = ħ/2). Moreover, the Compton horizon is spatially resolved as a point of equilibrium against an impenetrable, dynamically induced repulsive barrier. Building upon this fundamental localization limit, the invariant quantum phase is redefined as a latent rotational bivector confined within the spatiotemporal plane. Under relative motion, the Lorentz transformation projects this temporal kinematics into three-dimensional space, deterministically generating the emergent macroscopic wave behavior. Consequently, wave-particle duality and double-slit interference are formally resolved not as the superposition of physical waves, but as the spatial modulation of this geometric phase, dictated by the topological gauge of the macroscopic apparatus. Finally, at the macroscopic scale, introducing an inertial anisotropy between radial and transverse couplings allows the flat-space Cl(4,0) framework to exactly replicate phenomenological orbital kinematics, including perihelion precession. Together, these results establish the foundation for a unified geometric reinterpretation of phenomena historically partitioned between Quantum Mechanics and General Relativity.