Coherent Emergence: A Regularized Quantum Field Framework For The Electromagnetic Interaction

We present a self-consistent, non-equilibrium quantum field framework based on the paradigm of Coherent Emergence, wherein fundamental interactions are derived as scale-dependent macroscopic projections originating from a single underlying complex scalar coherence field ψ(x^μ) operating over a polarizable vacuum substrate. Rather than postulating gauge fields top-down, we incorporate a finite phase-memory relaxation retardation lag T into the continuous manifold bulk, mapping the structural vacuum updates directly onto non-equilibrium transport equations. By evaluating the explicit tensor contractions over the internal non-isotropic phase-gradient metric cells, we prove that the spatial lattice blocks experience a geometric compression that shifts the primary kinetic scaling factor identically to a parameter-free value of $9/2$, while the localized scalar mass channel preserves its canonical $1/2$ unit basis. Symmetrically, when external electrodynamic perturbations drive the vacuum canvas out of local stationarity, the irreversible energy-loss budget is resolved via the non-equilibrium statistical mechanics of the quantum substrate. Utilizing the Furutsu-Novikov functional theorem alongside the Kubo fluctuation-dissipation theorem, we demonstrate that a third-order spatiotemporal time-derivative regularizing term is dynamically generated within the effective action. This higher-order transport source compiles into a macro-coefficient factor of exactly $5/2$, acting as a supersonic spectral cutoff that successfully insulates the electrodynamic sector against ultraviolet divergence loops without ad-hoc parameter fine-tuning. The resulting Master Maxwell-Cattaneo-Vernotte transport engine dictates that the classical Maxwell equations are a compulsory, mathematically closed macroscopic consequence of the quantized underlying transport substrate, providing a pristine, non-singular foundation for the subsequent quantum induction of background spatiotemporal geometries.