Definitive Proof of the Existence of Quantum Yang-Mills with Mass Gap: Spectral Architecture, Noncommutative Geometry, and Fundamental Impacts
Year: 2025
Type: article
Abstract: We rigorously prove the existence of quantum Yang-Mills theory with a compact non-Abelian gauge group and a positive mass gap, thus resolving the Clay Millennium Problem. Our approach combines spectral analysis, noncommutative geometry, and random matrix theory to construct a discrete spectral architecture that ensures a uniform mass gap, compatible with the Osterwalder–Schrader axioms and Connes’ framework. This work establishes a new paradigm for the unification of geometry, spectral theory, and quantum physics, with deep implications for the understanding of confinement, the emergence of spacetime, and the arithmetic structure of spectra.
Author: VIEIRA, PAULO HENRIQUE
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6930803520
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