| _version_ | 1866901338385809408 |
|---|---|
| author | Caffagni, Andrea |
| author_facet | Caffagni, Andrea |
| contents | <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> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19641064 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Hamiltonian Reduction, Dual-Entropy Lyapunov Control, and the Yang–Mills Mass-Gap Problem Caffagni, Andrea Yang-Mills mass gap Lattice gauge theory Hamiltonian lattice Yang-Mills Osterwalder-Schrader reconstruction Renormalization group, block-spin transformations Modified log-Sobolev inequality Approximate tensorization of entropy Polchinski equation, multiscale Bakry-Émery Kotecký-Preiss polymer expansion Reflection positivity, transfer matrix <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> |
| title | Hamiltonian Reduction, Dual-Entropy Lyapunov Control, and the Yang–Mills Mass-Gap Problem |
| topic | Yang-Mills mass gap Lattice gauge theory Hamiltonian lattice Yang-Mills Osterwalder-Schrader reconstruction Renormalization group, block-spin transformations Modified log-Sobolev inequality Approximate tensorization of entropy Polchinski equation, multiscale Bakry-Émery Kotecký-Preiss polymer expansion Reflection positivity, transfer matrix |
| url | https://doi.org/10.5281/zenodo.19641064 |