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| Format: | Recurso digital |
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Zenodo
2025
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| Accés en línia: | https://doi.org/10.5281/zenodo.17067828 |
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- <p><strong>Abstract.</strong><br>We study 4D Yang–Mills in a lattice operator-algebra framework with an ultra-local, gauge-invariant, time-reflection-symmetric scroll-lock deformation of engineering dimension <span><span>Δ>4\Delta > 4</span><span><span><span>Δ</span><span>></span></span><span><span>4</span></span></span></span>. We prove uniform one-block spectral gaps for the transfer kernel, polymer activity bounds satisfying Kotecký–Preiss with explicit constants, and exponential clustering. We provide a constructive Mosco recovery sequence and upgrade to norm–resolvent convergence, yielding a continuum Hamiltonian <span><span>HH</span><span><span><span>H</span></span></span></span> with a nonzero gap <span><span>χ0>0\chi_0 > 0</span><span><span><span><span>χ</span><span><span><span><span><span><span>0</span></span></span><span></span></span></span></span></span><span>></span></span><span><span>0</span></span></span></span>, independent of the lattice spacing <span><span>aa</span><span><span><span>a</span></span></span></span>. We then establish (i) reflection positivity for the Wilson+scroll measure, (ii) OS-limit existence with Euclidean invariance and cluster properties, (iii) OS→Wightman reconstruction giving a unitary, positive-energy Poincaré representation with unique vacuum, and (iv) mass-gap transfer <span><span>m0≥χ0m_0 \ge \chi_0</span><span><span><span><span>m</span><span><span><span><span><span><span>0</span></span></span><span></span></span></span></span></span><span>≥</span></span><span><span><span>χ</span><span><span><span><span><span><span>0</span></span></span><span></span></span></span></span></span></span></span></span> via the Källén–Lehmann spectral measure. Finally, we prove <span><span>O(4)O(4)</span><span><span><span>O</span><span>(</span><span>4</span><span>)</span></span></span></span> restoration/Lorentz invariance through Symanzik power counting for irrelevant operators, and couple the theory to a background metric to recover the stress–energy Ward identity and the YM trace anomaly. All constants controlling decay and gaps depend only on the group <span><span>GG</span><span><span><span>G</span></span></span></span>, dimension <span><span>d=4d = 4</span><span><span><span>d</span><span>=</span></span><span><span>4</span></span></span></span>, coarse scale <span><span>L≥L⋆L \ge L_\star</span><span><span><span>L</span><span>≥</span></span><span><span><span>L</span><span><span><span><span><span><span>⋆</span></span></span><span></span></span></span></span></span></span></span></span>, and scroll amplitude; they are uniform in <span><span>a↓0a \downarrow 0</span><span><span><span>a</span><span>↓</span></span><span><span>0</span></span></span></span>.</p> <p><strong>Key contributions.</strong></p> <ul> <li> <p>Reflection positivity for Wilson+scroll action; OS axioms verified uniformly.</p> </li> <li> <p>Explicit Kotecký–Preiss bounds with constants; exponential clustering.</p> </li> <li> <p>Constructive Mosco recovery sequence ⇒ strong → norm–resolvent convergence.</p> </li> <li> <p>Uniform transfer-operator gap ⇒ continuum mass gap <span><span>m0≥χ0m_0 \ge \chi_0</span><span><span><span><span>m</span><span><span><span><span><span><span>0</span></span></span><span></span></span></span></span></span><span>≥</span></span><span><span><span>χ</span><span><span><span><span><span><span>0</span></span></span><span></span></span></span></span></span></span></span></span>.</p> </li> <li> <p><span><span>O(4)O(4)</span><span><span><span>O</span><span>(</span><span>4</span><span>)</span></span></span></span> restoration and Lorentz invariance in the continuum limit.</p> </li> <li> <p>Metric coupling recovers stress–energy Ward identity and YM trace anomaly.</p> </li> <li> <p>Appendix H supplies all previously sketched steps in full detail (RP lemma, RG block-gap persistence, mixing ⇒ spectral gap, OS→Wightman continuation, anomaly normalization).</p> </li> </ul> <p> </p>