Resolution to the Yang–Mills Existence and Mass Gap Problem

Abstract:This paper presents a rigorous non-perturbative construction of quantum Yang-Mills theory in four-dimensional Euclidean space ℝ⁴ with compact gauge group SU(N), satisfying all conditions outlined by the Clay Mathematics Institute for the Millennium Prize Problem. Using the Osterwalder–Schrader axioms and path integral quantization, we construct a valid Euclidean QFT and prove the existence of a strictly positive mass gap (Δ > 0). Key contributions:- Verification of all OS axioms (reflection positivity, clustering, Euclidean invariance)- Formal reconstruction of Wightman QFT with a bounded Hamiltonian spectrum- Spectral decay of correlation functions, leading to a non-zero mass gap- Gauge-fixing via Faddeev–Popov and Gribov–Zwanziger horizon constraint- Explicit mathematical theorems and operator proofs for mass gap existence This paper is submitted for academic peer review and public scrutiny as a complete and original resolution to one of the most critical open questions in theoretical physics. 📂 Keywords:Yang-Mills Theory, Mass Gap, Quantum Field Theory, Osterwalder–Schrader Axioms, Clay Millennium Problem, Gauge Theory, SU(N), Functional Integration, Spectral Gap, Non-Abelian Fields, Gribov Ambiguity, Wightman Reconstruction, Lattice QFT