Covariant Quantum-Corrected Gravitational Deflection: Effective Action Principle, Hadamard Bitensor Reduction, and Observational Dispersion Bounds

Abstract: We formulate a mathematically rigorous, covariant effective field theory governing the weak-field gravitational deflection of light with leading-order quantum dispersive corrections. To resolve legacy foundational inconsistencies—specifically, unphysical zero-cancellation of transverse ray acceleration in isotropic coordinates, time-divergent 4D spacetime integrals for static sources, and dimensional mismatches in phenomenological coupling parameters—we construct a covariant action principle coupling a mediating vector field \psi_\mu to static matter and electromagnetic field tensors through a gauge-invariant dimension-6 effective operator. Using the Hadamard Green's bitensor formalism, we analytically collapse the 4D spacetime volume integral onto the photon's 1D null trajectory, eliminating secular temporal divergences. By evaluating the metric Christoffel symbols in isotropic Cartesian coordinates, we prove that temporal (g_{00}) and spatial (g_{xx}) metric curvature components contribute constructively, resolving the legacy sign cancellation bug. The master deflection formula is derived with the exact geometric normalization prefactor 1/(32\pi): \delta\theta = \frac{4GM}{c^2 b} \left[ 1 + \alpha_{QG} \left(\frac{\ell_P}{b}\right)^2 \right] In the classical correspondence limit (\hbar \to 0), the framework identically recovers Einstein's general-relativistic deflection \Delta\theta_{GR} = 4GM/(c^2 b). The quantum-gravitational correction scales quadratically with the Planck length \ell_P = \sqrt{\hbar G/c^3}, yielding an ultra-suppressed, non-divergent correction (~ 10^{-75} rad for solar grazing rays) that strictly respects modern Cassini spacecraft radio astrometry bounds (|\gamma - 1| \le 2.3 \times 10^{-5}) while predicting testable Planckian deviations in primordial micro-black-hole lensing regimes. Inventor's Statement of Theoretical Innovation: • Author: Navneet Dwivedi (Independent Innovator) • Author Status: Independent Innovator (12th Grade / High School Background) • Background: 11-Year Hiatus from Formal Mathematics and Physics • Originality Declaration: This theoretical framework, covariant 4D-to-1D trajectory reduction, geometric factor derivation, and quantum dispersion formulation represent entirely original investigation by Navneet Dwivedi. The system reconciles vector-mediated gravitational perturbation models with general relativity without ad-hoc empirical parameter tuning. Submitted openly for formal scientific scrutiny, peer evaluation, and academic review.