Wave Unified Field Theory Solution to the Yang–Mills Mass Gap Problem

The Yang–Mills mass gap problem is one of the most famous unsolved Millennium Prize Problems in fundamental theoretical physics. Traditional Yang–Mills gauge field theory faces two core paradoxes: theoretical derivation predicts massless gauge bosons, while experimental observations prove relevant gauge particles have non-zero mass; meanwhile, low-energy non-perturbative calculation produces serious infrared divergence, leading to unstable mathematical solutions. Based on the self-established Wave Unified Field Theory (WUFT) and Unified Density Wave Field Theory (UDWFT), this paper retains the four original core equations completely consistent with the published theoretical framework. A group of derived auxiliary equations with unified writing style are constructed to match gauge field dynamics. By introducing wave field density condensation term and spacetime density gradient correction term into the Yang–Mills system, this research realizes natural mass generation for gauge bosons, eliminates infrared divergence, and achieves overall mathematical self-consistency and effective renormalization. This work provides a fundamental and systematic theoretical solution to the Yang–Mills mass gap problem.