Bridging Continuum Electrodynamics and High-Energy Physics: A Unified Solution Strategy for Elementary Particle Self-Confinement and Mass Generation via the LIFE Framework

Modern high-energy physics, anchored by the Standard Model and facilities such as CERN's Large Hadron Collider (LHC), successfully catalogues elementary particles and gauge interactions. However, the framework relies heavily on abstract quantum fields, phenomenological confinement models (such as MIT bag constants), and unexplainable free parameters (such as the nine disparate Yukawa mass couplings). Furthermore, classical electrodynamics and quantum field theory remain plagued by fundamental singularities: infinite point-charge self-energies and outward Coulomb explosion pressures requiring unphysical Poincaré stresses. This paper presents a comprehensive solution strategy based on the Local Interaction Field Equilibrium (LIFE) framework. By expanding Minkowski spacetime into a unified four-dimensional volumetric force-density continuum, we demonstrate that elementary particles (leptons and hadrons) and gauge bosons are not dimensionless point singularities, but stable, self-bound three-dimensional electromagnetic cavity eigenmodes. Through rigorous analytical and computational verification, we show that standing-wave envelope modulation combined with an inward gravito-inertial coupling term naturally resolves self-energy divergences, eliminates the Higgs hierarchy problem through geometric cavity scaling, and yields parameter-free quantum mass spectra governed by spherical Bessel functions.