The Quantized Fractal Equation (QFE) Revised: A UV-Finite Unified Theory via Fractional Dynamics and Ghost Compensation

This paper presents the Quantized Fractal Equation (QFE) , a novel unified field theory that seeks to reconcile quantum mechanics, General Relativity (GR), and the Standard Model. This framework utilizes Lorentz-invariant fractional differential operators (□ β/2 ) ,and incorporates a crucial Fractional Ghost Compensation Term (L NL Ghost) . The introduction of this term, inspired by higher-derivative theories, ensures the cancellation of ultraviolet (UV) divergences in the graviton propagator, rendering the theory UV-finite. Furthermore, the action includes a nonlinear density-dependent term F(ρ) leading to a Big Bounce scenario , and integrates all fundamental interactions under a single fractional covariant derivative . The theory maintains local gauge invariance through a non-local compensation mechanism and makes testable predictions regarding a minor violation of Lorentz Invariance (LIV) at high energies.