Fractal Resonance and the Emergence of Charge: Energy–Charge Duality in UFQFT

In the Unified Fractal Quantum Field Theory (UFQFT), all physical entities emerge from two interdependent fields: the energy field (Φ) and the charge field (Ψ). While conventional quantum field theories treat charge as a fundamental property, UFQFT reinterprets it as a derived feature of energy. Specifically, charge arises from phase asymmetries and directional resonances within the fractal geometry of the energy field. We formalize this relationship by introducing transformation equations between Φ and Ψ, demonstrating that Ψ ∝ R α ∇ φ , where R is the amplitude and φ the phase of Φ. This framework naturally accounts for fractional charges of quarks as rational winding numbers in fractal spacetime and explains neutral composites, such as the neutron, as states of phase cancellation. Applications to electron stability, quark charge distribution, and proton–neutron binding are explored, including a case study of the deuteron’s 2.2 MeV binding energy. The results suggest that charge is not an independent quantity but an emergent geometric property of energy resonances. This reinterpretation provides a new foundation for particle physics, with implications for unification, nuclear structure, and the nature of fundamental interactions.