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| Format: | Recurso digital |
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Zenodo
2026
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| Hasła przedmiotowe: | |
| Dostęp online: | https://doi.org/10.5281/zenodo.18988568 |
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Spis treści:
- <p>We prove that for any compact simple gauge group G, pure Yang–Mills theory<br>in four Euclidean dimensions has a rigorous construction satisfying the Wightman<br>axioms, with a mass gap ∆ > 0 and a non-trivial vacuum sector (not a generalized<br>free field).<br>Three key innovations drive the proof. First, the hyperoctahedral group W (B4)<br>(the symmetry of the 4D hypercubic lattice, |W | = 384) reduces the infinite-<br>dimensional coupling space to exactly 30 gauge-invariant operators through dimen-<br>sion 8 — a group-independent reduction. Second, the renormalization-group coars-<br>ening Jacobian satisfies a scheme-independent polynomial inequality J2(u) > 1 for<br>all u > 0, following from positivity of the first two universal beta-function coeffi-<br>cients. Third, three arguments — the polynomial bound, Watson–Nevanlinna–Sokal<br>Borel summability, and a derived cluster expansion — combine sequentially to cover<br>the full coupling range, with an explicit finite-step migration lemma connecting the<br>weak-coupling Borel regime to the strong-coupling cluster expansion.<br>The proof invokes three external theorems: Watson–Nevanlinna–Sokal (complex<br>analysis), Osterwalder–Schrader reconstruction (axiomatic QFT), and Balaban’s<br>block-spin structural result (constructive QFT). All premises of these theorems are<br>derived from first principles.<br>MSC 2020: 81T13, 81T25, 22E70.<br>Keywords: Yang–Mills, mass gap, lattice gauge theory, Borel summability, con-<br>structive quantum field theory, B4 root system.</p>