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2026
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| Online-Zugang: | https://doi.org/10.5281/zenodo.20134147 |
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| _version_ | 1866901579502714880 |
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| author | jiazheng liu |
| author_facet | jiazheng liu |
| contents | <p>This manuscript is a student- verification edition of the global heat- semigroup equivalence theorem for two explicitly defined radial operators. The causal operator is</p> <p> </p> <p>A_{\mathrm{caus}} = \sqrt{-\Delta_{S^2} + \frac{1}{4}}</p> <p> </p> <p>on L^2 (S^2, d\Omega) . The Yang- Mills radial operator is</p> <p> </p> <p>A_{\mathrm{YM}} = \frac{N + 1}{2}</p> <p> </p> <p>on the direct sum of the fixed- number Schwinger oscillator spaces. The proof is expanded as a calculation manual: every definition, algebraic substitution, index rename, commutator expansion, geometric- series identity, positivity calculation, and spectral comparison is written as a checkable chain. The final theorem proved here is the global equality of the heat semigroups of the two radial constructions, equivalently the unitary equivalence of the two radial operators. This text deliberately avoids using BRST compatibility and avoids using Taylor's Landau- gauge theorem as a proof ingredient. They are not needed for the radial heat- semigroup statement.</p> <p> </p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20134147 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Heat Semigroup Global EquivalenceStudent Verification EditionA Fully Expanded Calculation Manual for the Radial- Operator Theorem jiazheng liu <p>This manuscript is a student- verification edition of the global heat- semigroup equivalence theorem for two explicitly defined radial operators. The causal operator is</p> <p> </p> <p>A_{\mathrm{caus}} = \sqrt{-\Delta_{S^2} + \frac{1}{4}}</p> <p> </p> <p>on L^2 (S^2, d\Omega) . The Yang- Mills radial operator is</p> <p> </p> <p>A_{\mathrm{YM}} = \frac{N + 1}{2}</p> <p> </p> <p>on the direct sum of the fixed- number Schwinger oscillator spaces. The proof is expanded as a calculation manual: every definition, algebraic substitution, index rename, commutator expansion, geometric- series identity, positivity calculation, and spectral comparison is written as a checkable chain. The final theorem proved here is the global equality of the heat semigroups of the two radial constructions, equivalently the unitary equivalence of the two radial operators. This text deliberately avoids using BRST compatibility and avoids using Taylor's Landau- gauge theorem as a proof ingredient. They are not needed for the radial heat- semigroup statement.</p> <p> </p> |
| title | Heat Semigroup Global EquivalenceStudent Verification EditionA Fully Expanded Calculation Manual for the Radial- Operator Theorem |
| url | https://doi.org/10.5281/zenodo.20134147 |