What does this research mean for the field?

Pure quantum Yang-Mills theory on ℝ4 for any compact simple gauge group G globally exists and possesses a strictly positive spectral mass gap. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

Prove the global existence and strictly positive spectral mass gap of pure four-dimensional quantum Yang-Mills theory on ℝ4 for any compact simple gauge group.

August 30, 2026Open Access

Existence and Mass Gap of 4D Quantum Yang-Mills Theory via Gribov Horizon Localization

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Authors

CNCharles EDOU NZE

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Implication

Theoretical analysis demonstrates a non-zero mass gap in four-dimensional quantum Yang-Mills theory, indicating resolution of the Millennium Prize problem.

Key Points

Prove the global existence and strictly positive spectral mass gap of pure four-dimensional quantum Yang-Mills theory on ℝ4 for any compact simple gauge group.
Restricted functional integration to the fundamental Gribov region to eliminate gauge copies and localized the restriction via auxiliary ghost fields in the Gribov-Zwanziger formalism.
Proved all-order renormalizability using the algebraic renormalization method and Slavnov-Taylor identities.
Formally certified the spectral mass gap condition and strict positivity of physical excitation states in Lean 4 via Mathlib with zero unproven axioms.
Dynamically generated a positive Gribov mass parameter (γ > 0) proportional to ΛQCD via the horizon condition, shifting gluon propagator poles and suppressing zero-momentum propagation.
Established a strictly positive spectral mass gap above the quantum vacuum satisfying Δ ≥ √2 g √Nc γ² > 0.

Cite This Study

Charles EDOU NZE (2026) studied this question.

synapsesocial.com/papers/6a93f0b06c1a8fb52e79d0ca https://doi.org/10.5281/zenodo.22149027

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Implication

Theoretical analysis demonstrates a non-zero mass gap in four-dimensional quantum Yang-Mills theory, indicating resolution of the Millennium Prize problem.

Existence and Mass Gap of 4D Quantum Yang-Mills Theory via Gribov Horizon Localization

Discussion

Member takes

Implication

Key Points

Cite This Study

Existence and Mass Gap of 4D Quantum Yang-Mills Theory via Gribov Horizon Localization

Discussion

Member takes

Implication

Key Points

Cite This Study

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