A Formal Proof of the Yang--Mills Mass Gap in Quantum Gauge Theory
Fuente:
Zenodo
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Recurso digital |
| Veröffentlicht: |
Zenodo
2025
|
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866901492587298816 |
|---|---|
| author | Erga, Cato |
| author_facet | Erga, Cato |
| contents | <p>This paper presents a fully explicit and self-contained proof of the Yang–Mills mass gap problem, formulated using formal quantum gauge theory and operator-valued field constructions.</p> <p>It establishes the existence of a nonzero mass gap <span><span>m=0.5m = 0.5</span><span><span><span>m</span><span>=</span></span><span><span>0.5</span></span></span></span> in a quantum Yang–Mills theory over <span><span>SU(N)SU(N)</span><span><span><span>S</span><span>U</span><span>(</span><span>N</span><span>)</span></span></span></span>, satisfying all Wightman axioms, BRST cohomological conditions, and lattice-to-continuum consistency.</p> <p>Supporting sections include:<br>– Spectral density via Källén–Lehmann representation<br>– BRST cohomology: <span><span>ψ(x)=e−x2∈kerQ∖im Q\psi(x) = e^{-x^2} \in \ker Q \setminus \mathrm{im}\, Q</span><span><span><span>ψ</span><span>(</span><span>x</span><span>)</span><span>=</span></span><span><span><span>e</span><span><span><span><span><span><span>−<span>x</span><span>2</span></span></span></span></span></span></span></span><span>∈</span></span><span><span>ker</span><span>Q</span><span>∖</span></span><span><span><span>im</span></span><span>Q</span></span></span></span><br>– Taylor convergence from Wilson action to continuum Yang–Mills<br>– Appendix with full supporting lemmas</p> <p>All symbolic dependencies are resolved, and the proof is presented in academic LaTeX format with glossary and references.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_15825398 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | A Formal Proof of the Yang--Mills Mass Gap in Quantum Gauge Theory Erga, Cato <p>This paper presents a fully explicit and self-contained proof of the Yang–Mills mass gap problem, formulated using formal quantum gauge theory and operator-valued field constructions.</p> <p>It establishes the existence of a nonzero mass gap <span><span>m=0.5m = 0.5</span><span><span><span>m</span><span>=</span></span><span><span>0.5</span></span></span></span> in a quantum Yang–Mills theory over <span><span>SU(N)SU(N)</span><span><span><span>S</span><span>U</span><span>(</span><span>N</span><span>)</span></span></span></span>, satisfying all Wightman axioms, BRST cohomological conditions, and lattice-to-continuum consistency.</p> <p>Supporting sections include:<br>– Spectral density via Källén–Lehmann representation<br>– BRST cohomology: <span><span>ψ(x)=e−x2∈kerQ∖im Q\psi(x) = e^{-x^2} \in \ker Q \setminus \mathrm{im}\, Q</span><span><span><span>ψ</span><span>(</span><span>x</span><span>)</span><span>=</span></span><span><span><span>e</span><span><span><span><span><span><span>−<span>x</span><span>2</span></span></span></span></span></span></span></span><span>∈</span></span><span><span>ker</span><span>Q</span><span>∖</span></span><span><span><span>im</span></span><span>Q</span></span></span></span><br>– Taylor convergence from Wilson action to continuum Yang–Mills<br>– Appendix with full supporting lemmas</p> <p>All symbolic dependencies are resolved, and the proof is presented in academic LaTeX format with glossary and references.</p> |
| title | A Formal Proof of the Yang--Mills Mass Gap in Quantum Gauge Theory |
| url | https://doi.org/10.5281/zenodo.15825398 |