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| Hovedforfatter: | |
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| Format: | Recurso digital |
| Sprog: | engelsk |
| Udgivet: |
Zenodo
2025
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| Fag: | |
| Online adgang: | https://doi.org/10.5281/zenodo.17190165 |
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Indholdsfortegnelse:
- <p><strong>My name is Matthew William Maloney, I am an independent researcher from Columbus, Mississippi.</strong></p> <p>In this preprint, I rigorously address the Clay Millennium Problem on the Yang–Mills mass gap. A four-dimensional pure SU(N) Yang–Mills quantum field theory is constructed for all N ≥ 2 in a nonperturbative lattice setting. The resulting theory satisfies the Osterwalder–Schrader (OS) axioms and the Wightman axioms and exhibits a strictly positive spectral (mass) gap.</p> <p><strong>Logical path to the gap:</strong></p> <ol> <li> <p>Exact planar blocking: one finite-depth block enforces mesoscopic time t′ ≥ t*.</p> </li> <li> <p>Planar sandwich inequality: K(t_min) >= K_plane(t′) >= K(t_max), with t_min = t′ and t_max = 9 t′ + 4 beta_dim.</p> </li> <li> <p>Doeblin minorization: strengthens the lower bound with c_mix > 1.</p> </li> <li> <p>Two-time one-tile penalty: center-twist projection enforces rho_square < 1.</p> </li> <li> <p>Chessboard estimate: promotes to a uniform positive sheet tension.</p> </li> <li> <p>Loop–sheet inequality: sheet tension ⇒ area law for Wilson loops.</p> </li> <li> <p>Exponential clustering: reflection positivity plus the area law ⇒ uniform clustering.</p> </li> <li> <p>Transfer matrix: clustering implies a strictly positive spectral gap.</p> </li> <li> <p>Continuum passage: uniform constants persist as a → 0, so OS0–OS4 hold and OS→Wightman reconstruction yields a Haag–Kastler net with a positive gap.</p> </li> </ol> <p><strong>Key input:</strong> A uniform positive free-energy cost per unit area for inserting a nontrivial Z_N ’t Hooft center twist across a planar sheet (the “sheet tension”).</p> <p>From the sheet tension an area law for Wilson loops is established, and OS reconstruction yields exponential clustering and a uniform mass gap in the continuum.</p> <p><strong>SU(3) specialization:</strong> Explicit constants and numerical estimates appear in the companion paper, including the constructive glueball bound m0++ ≥ 1.106 sqrt(sigma).<br>M. W. Maloney, <em>Center–Twist Sheet Tension, Area Law, and a Mass–Gap Route for Pure SU(3) in Four Dimensions</em>, Zenodo (2025), <a href="https://doi.org/10.5281/zenodo.16909309">DOI: 10.5281/zenodo.16909309.</a></p> <p><strong>General G:</strong> The framework extends to all compact simple gauge groups, including centerless cases (G2, F4, E8) via a shifted heat-kernel flux-sheet construction.</p>