Nouman Theory I: A Two-Phase Solitonic Model for Wave–Particle Duality with a Characteristic Localization Length

This paper introduces a field-theoretic framework for wave–particle duality in which matter is described by a complex scalar field ψ carrying a conserved U(1) chargeIn the particle phase, the field condenses into a compact non-topological soliton (a Q-ball) with effective radius L ≈ r₀. In the wave phase, the same energy delocalizes in space and the field equation approaches the linear Klein–Gordon regime