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2025
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| Online Access: | https://doi.org/10.5281/zenodo.17401518 |
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| author | Arneth, Borros |
| author_facet | Arneth, Borros |
| contents | <p><span lang="EN-US">We present a unified formalism in which the familiar entities of spacetime, matter, gauge fields and the Standard Model emerge as <strong>projective images</strong> of a deeper state space — the <em>Diagram Hilbert Space</em> HD</span><span lang="EN-US">. We begin by providing rigorous definitions of HD</span><span lang="EN-US">, its associated operator algebra (topological, adjacency, relinking), and an internal “diagram-time” ordering parameter. We then define a family of projectors</span><span lang="EN-US"> mapping HD </span><span lang="EN-US">into emergent subspaces and show how spacetime metric, energy, mass and gauge charges are constructed from diagrammatic correlators. We further derive how the internal topology operators give rise to the SU(3)×SU(2)×U(1) structure of the Standard Model via automorphisms of diagram connectivity, and how the Higgs mechanism appears naturally as a projective alignment operator mediating between matter and spacetime sectors. The mathematical framework includes a variational principle for projection-entropy that yields Einstein-type dynamics, an information-geometric treatment of running couplings (via Fisher metric on parameter space), and a toy graph model for numerical exploration. The result is a coherent mathematical proposal that embeds both geometry and particle physics in one relational structure.</span></p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17401518 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | A Diagram-Hilbert-Space Framework: Mathematical Foundations, Projection Mechanism and Emergence of the Standard Model Arneth, Borros <p><span lang="EN-US">We present a unified formalism in which the familiar entities of spacetime, matter, gauge fields and the Standard Model emerge as <strong>projective images</strong> of a deeper state space — the <em>Diagram Hilbert Space</em> HD</span><span lang="EN-US">. We begin by providing rigorous definitions of HD</span><span lang="EN-US">, its associated operator algebra (topological, adjacency, relinking), and an internal “diagram-time” ordering parameter. We then define a family of projectors</span><span lang="EN-US"> mapping HD </span><span lang="EN-US">into emergent subspaces and show how spacetime metric, energy, mass and gauge charges are constructed from diagrammatic correlators. We further derive how the internal topology operators give rise to the SU(3)×SU(2)×U(1) structure of the Standard Model via automorphisms of diagram connectivity, and how the Higgs mechanism appears naturally as a projective alignment operator mediating between matter and spacetime sectors. The mathematical framework includes a variational principle for projection-entropy that yields Einstein-type dynamics, an information-geometric treatment of running couplings (via Fisher metric on parameter space), and a toy graph model for numerical exploration. The result is a coherent mathematical proposal that embeds both geometry and particle physics in one relational structure.</span></p> |
| title | A Diagram-Hilbert-Space Framework: Mathematical Foundations, Projection Mechanism and Emergence of the Standard Model |
| url | https://doi.org/10.5281/zenodo.17401518 |