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
This resolution does not rely on perturbation, approximation, or renormalization. It defines the theory directly — not through speculative fields, but through measurable and enforceable structure.
The configuration space is not postulated. It is realized. The Hilbert space is not assumed. It is constructed. The Hamiltonian is not inferred. It is derived. And the spectrum reveals a gap — not through expectation, but by necessity.
Mass, in this framework, is not added. It emerges. From resonance. From geometry. From structural coercion that binds field to form.
Where physics hopes, structure compels.
If you are an arXiv member and believe this contribution deserves broader visibility, you may use the following endorsement code when supporting its publication:
Code: D9JE3Z
This is a one-time option to help open academic channels for independent, non-affiliated solutions.