A New Model of the Electron: A Dynamic Quantum Ring Singularity

To resolve the unphysical infinite density divergence of point-like electrons, this paper establishes a self-consistent hybrid model by synthesizing Einstein’s General Relativity (Kerr-Newman metric) with Dirac’s relativistic quantum mechanics. Using the fine-structure constant as a quantum-gravitational bridge, we derive the structural radius of the electron to be exactly a = 1.9307 x 10⁻¹³ m, establishing that the particle is fundamentally a curvilinear ring singularity. To regularize the spatial boundary without mathematical breakdowns, the sharp delta function is formalized via a smooth Gaussian representation, where epsilon acts as a small but strictly finite quantum cutoff scale. Upon 3D spatial probability normalization, the squaring of the wavefunction yields a regularized integral value, isolating the wave coefficient and maintaining quantum probability equilibrium (LHS = RHS = 1). Furthermore, a geometric charge current density integration proves that the total net charge invariantizes perfectly to Q_net = e. Finally, mapping this regularized state vector into the semi-classical Einstein field equations shows that the time-average energy-momentum expectation value naturally normalizes to M_e c², deriving a stable space-time background curvature under continuous ultra-high frequency Zitterbewegung oscillations.