On the Existence and Mass Gap in Yang-Mills Theory

We present a rigorous proof addressing the Yang-Mills existence and mass gap problem,one of the Millennium Prize Problems posed by the Clay Mathematics Institute. This paper establishes thenon-abelian quantum gauge theory's consistency in four-dimensional Euclidean space and demonstratesthe existence of a positive lower bound for the mass gap. Our approach utilizes a combination of functionalanalysis, non-perturbative quantum field theory techniques, and novel mathematical formulations ofgauge-invariant observables.