From Matter to Gauge Fields: Reactive Series and the Geometry of Wave Propagation

This paper presents a unified field-theoretic framework in which all gauge fields — including electromagnetic, gravitational, and matter waves — originate from closed surface structures representing material configurations. Field propagation is reinterpreted as a recursive chain of action and reaction, mathematically expressed by the converging series: Each term represents a delayed, phase-rotated, and attenuated geometric response to an initial deformation A. The scalar field φ thus encodes a memory of matter through structured wave propagation. Two orthogonal components govern physical behavior: φ₀ᵢ describes transverse waves that couple time and space — such as electromagnetic and gravitational waves. φᵢⱼ describes internal spatial interference — such as magnetic and matter waves. Wave attenuation, resonance, and geometric redirection arise naturally from this recursive process. All fields are shown to be spatially propagated echoes of material geometry, dissolving the traditional distinction between field and source. This formulation lays the groundwork for a unified geometric theory of physical interactions based on closed surface dynamics. Tetsuo Konno(今野哲夫) https://orcid.org/0009-0002-1842-7865