Ervin Goldfain. Fractional Field Theory as Self-organized Criticality (section I)
Natural Sciences / Physics / Mathematical Physics
Submitted on: Mar 06, 2026, 08:21:16
Description: We propose a unifying framework in which Fractional Field Theory emerges as macroscopic description of systems driven to Self-Organized Criticality (SOC) in continuous spacetime dimensions. Beginning with a definition of SOC beyond lattice models (Sec. II), we show that local threshold dynamics and slow driving generate a stationary state characterized by an emergent Cantor Dust geometry (Secs. IIIâE"IV). The resulting support carries a singular, scale-invariant measure whose fractal and multifractal properties are derived explicitly (Sec. V). Fields defined on this geometry necessarily obey nonlocal dynamics, governed by fractional Laplacians that arise uniquely as generators of anomalous diffusion (Sec. VI). We show that the associated propagators, dispersion relations, and scaling dimensions follow directly from the SOC geometry, without fine tuning or ad hoc assumptions. Applications to Particle Physics and Cosmology are developed in Sec. VII, including infrared mass generation, effective dark sectors, and modified gravitational dynamics. The framework is shown to be consistent with Effective Field Theory, the weak-field limit of General Relativity, and current observational bounds. Fractional Field Theory is thus an emergent description of critical spacetime geometry, rather than an extrapolation of relativistic Quantum Field Theory.