Artificial Intelligence and Electrical & Electronics Engineering: AIEEE Open Access
A Non-Perturbative Framework for the Yang-Mills Mass Gap in SU(3) Gauge Theory: From Lattice Regularization to Spectral Geometry
Abstract
Chur Chin
We develop a comprehensive and mathematically rigorous framework for addressing the Yang–Mills mass gap problem in SU(3) gauge theory, one of the Clay Millennium Prize Problems. Our approach synthesizes lattice gauge theory, instanton calculus, spectral analysis, and geometric methods to construct a non-perturbative formulation of four- dimensional Yang–Mills theory that satisfies the Osterwalder–Schrader (OS) axioms. We demonstrate, both analytically and numerically, the existence of a positive spectral gap between the vacuum and the first excited state. Using Wilson loop area laws, heat kernel bounds, and topological susceptibility, we extract mass estimates for glueball states and establish confinement as a physical manifestation of the mass gap. Additionally, we explore symmetry transitions (SU(3) → SU(2) → U(1)), trace anomalies, and holographic dualities to deepen the physical and topological understanding of the gap structure. This work offers a clear roadmap toward a constructive proof of the Yang–Mills mass gap, combining quantum field theory, differential geometry, and lattice simulation into a unified treatment.