Relative Field Localization (RFL): Applications to Contact, Material Density, Thermal Transport, and Light–Matter Interaction

This paper presents an integrated field-theoretic investigation of Relative Field Localization (RFL) and its proposed applications to material contact, nonlinear repulsion, density-dependent interactions, layered mechanical resistance, thermal transport, fluid circulation, and light–matter interactions. The study develops a scalar-field overlap model containing quartic and sextic nonlinear contributions. For two nonnegative, in-phase overlapping field profiles, the interaction energy is derived by subtracting the isolated self-energies. The resulting expression contains competing attractive and repulsive contributions. A Gaussian variational calculation provides closed-form overlap integrals and a conditional short-separation criterion for sextic repulsion to dominate. The paper extends the analysis to material contact and interfacial pressure, distinguishing microscopic field-response attenuation from macroscopic mechanical stress and force balance. It also separates number density, mass density, RFL charge density, and field-energy density, examining their respective roles in material response. The thermal analysis distinguishes radiative transfer, conduction, and convection, and formulates the proposed RFL interpretation of temperature-dependent field responses and fluid circulation. The light–matter sections examine conditional electromagnetic coupling, causal optical response, refraction, elastic and inelastic scattering, absorption, emission, and atomic transitions. Energy–momentum conservation and Compton-scattering kinematics are treated as consistency requirements. The manuscript distinguishes exact mathematical identities, conditional derivations, phenomenological models, and open physical hypotheses. Its purpose is to establish a unified mathematical framework for investigating these applications while identifying the additional microscopic derivations and experimental tests required to validate the proposed mechanisms. It does not claim that all proposed material mechanisms have already been experimentally established.