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

We present a self-consistent, non-equilibrium quantum field framework based on the paradigm of Coherent Emergence, wherein the weak interaction and its unique symmetry-breaking signatures are derived as scale-dependent macroscopic projections originating from a single underlying complex scalar coherence field ψ(x^μ) operating over a polarizable vacuum medium. Rather than postulating abstract local SU(2)L × U(1)Y gauge groups 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 a stable, stationary phase-vortex lepton core configuration under extreme sub-atomic compression, we demonstrate that the spin-curvature constraints of the vacuum lattice naturally generate a local chiral projection layer via the time-like Dirac matrix algebra, forcing maximal parity violation strictly from first principles. When external high-frequency sub-atomic deformations drive the vacuum canvas out of local stationarity, the irreversible energy-loss budget is resolved via the non-equilibrium statistical field mechanics of the quantum substrate. Utilizing the Furutsu-Novikov functional theorem alongside the Kubo fluctuation-dissipation theorem, we prove that a third-order spatiotemporal time-derivative regularizing term is dynamically generated within the effective action. Due to the spatial trace contraction over the dual chiral phase-vortex cells active inside the sub-atomic core, this regularizing source compiles into an exact, parameter-free macro-coefficient factor of $6/2$, providing a supersonic spectral cutoff that successfully insulates the weak sector against ultraviolet divergence loops. The resulting Master Maxwell-Cattaneo-Vernotte transport engine dictates that the fundamental Fermi coupling constant GF is rigorously locked to the vacuum transport inertia, while the global phase-invariance of the finalized action yields a formal mathematical proof for the conserved vector current (CVC) hypothesis directly from first principles.