The Yang–Mills Existence and Mass Gap problem lies at the intersection of quantum field theory and mathematics. It seeks to establish a rigorous foundation for Yang–Mills theory, which underpins the Standard Model of particle physics.
The challenge is to show that for any compact simple gauge group, a non-trivial quantum Yang–Mills theory exists on ℝ⁴ and exhibits a mass gap — meaning that the lowest possible energy state above the vacuum has strictly positive energy.
Resolving this would bridge a fundamental gap between physics and pure mathematics, confirming key aspects of quantum behavior through mathematical rigor.
Source: Clay Mathematics Institute – Yang–Mills and Mass Gap
The approach developed here examines the Yang–Mills mass gap through structural resonance rather than perturbation or renormalization. The framework constructs the configuration space, Hilbert space, and Hamiltonian directly from structural principles — without postulating field behavior in advance.
Within this construction, the mass gap emerges as a structural consequence rather than an assumption. Details will be made available upon publication.