Phase Closure and the Geometric Origin of Mass A Variational Approach to Quantum Dynamics

We propose a minimal process-based framework in which physical quantities arise from constraints on phase evolution in spacetime. Matter is identified with topologically closed phase configurations satisfying a quantization condition H dϕ = 2πn. Within this framework, mass is not a fundamental parameter but a geometric property associated with the inverse characteristic scale of phase closure, m = ℏ/(cR0). A single variational principle applied to the phase field yields the Klein–Gordon equation in the relativistic regime and the Schrödinger equation in the non-relativistic limit. Local phase invariance naturally leads to gauge interactions. The approach eliminates point-like singularities and recasts mass, inertia, and interaction fields as emergent features of phase topology.