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| Hovedforfatter: | |
|---|---|
| Format: | Recurso digital |
| Sprog: | engelsk |
| Udgivet: |
Zenodo
2026
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| Fag: | |
| Online adgang: | https://doi.org/10.5281/zenodo.19641064 |
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Indholdsfortegnelse:
- <p>We give a corrected finite-volume reduction of the Yang–Mills mass-gap problem and carry<br>out explicit calculations in the smallest genuinely nonabelian SU(2) active window. On the<br>finite-volume side we prove the exact gauge-invariant carrier grammar, exact electric-shell<br>diagonalization, the global quasi-momentum fiber decomposition, the spectator-first inactive<br>reduction, the active-image reduction, the scalar-vacuum reduction, and a direct strong-coupling<br>gap theorem.<br>We also prove the abstract infinite-volume/continuum transfer ladder: uniform finite-volume<br>gap bounds imply subsequential infinite-volume Euclidean decay, and any Osterwalder–Schrader<br>compatible continuum subsequential limit carrying the same physical mass lower bound inherits<br>a continuum mass gap.<br>The dissipative part of the manuscript is reorganized around two relative-entropy densities<br>for the blocked flow: a microscopic density, monotone under blocking by data processing, and<br>a coarse density, natural for local marginals, large-field control, and the blocked Euclidean-to<br>Hamiltonian dictionary. We prove the microscopic monotonicity theorem, a gauge-compatible<br>perturbative ultraviolet initialization theorem, an abstract coarse-entropy production formula, a<br>local entropy lift theorem under approximate tensorization, explicit Pinsker/subgaussian large<br>field and good-field estimates, and an observable-by-observable entropy-to-dictionary transfer<br>theorem.<br>At the fixed-spacing Euclidean/Hamiltonian interface we also prove that reflection positivity is<br>preserved by any blocking map that commutes with time reflection and preserves the positive-time<br>algebra. This internalizes the structural part of the Osterwalder–Schrader bridge.<br>The strongest closure theorem supported by the manuscript remains conditional. Along a<br>Hamiltonian-compatible continuum sequence, if one supplies the YM-specific dissipative/blocked<br>contour package — namely a gauge-compatible ultraviolet reference with ultraviolet control, a<br>coarse-entropy production theorem, a blocked local-lift theorem, an explicit entropy-to-dictionary<br>instantiation, and a quantitative blocked contour / PF-band theorem furnishing KP-small<br>phase/source envelopes together with the adapted open-cavity source estimate — together<br>with the finite torus certificate and the remaining algebra-identification part of the blocked<br>Hamiltonian/Osterwalder–Schrader bridge, then every corresponding continuum subsequential<br>limit in the first window has mass gap at least the prescribed target mass. For general compact<br>simple gauge groups, the remaining extension is reduced to a finite atlas package together with<br>the same dissipative, PF-band, and Euclidean/Hamiltonian inputs.</p>