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 depend on approximation or renormalization. It defines the theory directly — through measurable structure, not speculative fields.
The configuration space is not idealized, but realized. The Hilbert space is built. The Hamiltonian is constructed. And the spectrum reveals a gap not because it should — but because it must.
Mass here is not assumed. It is born from resonance, geometry, and coercion.
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