Solution to the Yang–Mills Mass Gap Problem via the Global Unified Wave Field and Spacetime Background Field Coupling Theory

This paper systematically resolves the classic Yang–Mills mass gap millennium problem and eliminates the inherent infrared divergence ambiguity existing in traditional non-Abelian gauge field theories. Based strictly on the axiomatic system of the Global Unified Wave Field and Spacetime Background Field Coupling Theory, this study reconstructs the complete dynamic framework of modified Yang–Mills gauge fields through variational derivation, field coupling decomposition, and dimensional regularization verification. Different from conventional Higgs spontaneous symmetry breaking mechanisms that rely on artificially introduced scalar fields and vacuum expectation values, the present model realizes intrinsic dynamic mass generation of gauge bosons purely through background field gradient coupling. This work completes the full mathematical derivation of modified covariant derivatives, revised gauge field Lagrangians, corrected propagator structures, and non-Abelian gauge invariance verification. All derivations maintain strict four-dimensional general covariance, energy–momentum conservation, and high-energy renormalizability. This paper additionally supplements a rigorous comparative derivation distinguishing background-field-induced dynamic mass generation from traditional spontaneous symmetry breaking. Combined with LHC experimental vector boson mass data, numerical parameter fitting and quantitative constraint calculations are performed, providing explicit falsifiable numerical bounds for the coupling parameters. The results completely eliminate low-energy infrared divergence, establish a mathematically rigorous mass gap origin mechanism, and form a self-consistent, fully computable, observationally consistent solution to the Yang–Mills mass gap problem. As an important branch and verification expansion of the Global Unified Wave Field Coupling theoretical system, this research further perfects the underlying logical foundation of quantum gauge field theory and provides a new fundamental paradigm for quantum gravity unification.