Quantum-Fractal Logical Framework for Yang-Mills Fields
Enrique Vidal Silvente · 2025
We extend our quantum-fractal logical framework to non-abelian gauge theories by formulating Yang-Mills fields as resonant modes of a fractal Hilbert space operator. Specifically, we introduce a self-adjoint fractal gauge operator whose eigenmodes encode SU(N) field configurations, derive the Yang-Mills equations from a resonance-based action principle, and provide a spectral proof of the mass gap. Numerical simulations for SU(2) lattice models validate confinement properties and glueball spectra. Our results offer a unified fractal-spectral approach to gauge theory and gravity.