| _version_ | 1866901209424592896 |
|---|---|
| author | Maloney, Matthew William |
| author_facet | Maloney, Matthew William |
| contents | <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> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17190165 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Heat Kernel Sandwich Yields Sheet Tension and a 4D Yang Mills Mass Gap Maloney, Matthew William yang mills Yang Mills theory Mass Gap lattice guage theory osterwalder-schrader axioms Wightman axioms sandwich heat kernel sandwich one-tile penalty reflection positivity area law wilson loops constructive quantum field theory nonperturbative methods center symmetry heat kernel Peter Weyl sheet tension planar sandwich Clay Institute Millennial Prize Yang Mills Mass Gap AET anchored expansion theory Clay Millennium Problem SU(3) Compact simple Lie groups <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> |
| title | Heat Kernel Sandwich Yields Sheet Tension and a 4D Yang Mills Mass Gap |
| topic | yang mills Yang Mills theory Mass Gap lattice guage theory osterwalder-schrader axioms Wightman axioms sandwich heat kernel sandwich one-tile penalty reflection positivity area law wilson loops constructive quantum field theory nonperturbative methods center symmetry heat kernel Peter Weyl sheet tension planar sandwich Clay Institute Millennial Prize Yang Mills Mass Gap AET anchored expansion theory Clay Millennium Problem SU(3) Compact simple Lie groups |
| url | https://doi.org/10.5281/zenodo.17190165 |