A Note on Derivative Hierarchy in Gauge Theory and Gravity: A Historical Supplement on Connection, Curvature, and Line-Integral Observables
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| Format: | Recurso digital |
| Language: | English |
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2026
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| _version_ | 1866902323414958080 |
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| author | Hanamura, Satoshi |
| author_facet | Hanamura, Satoshi |
| contents | <p>[41 Supplement]<br><br></p> <p>This supplementary note provides a historical and structural clarification of a largely unarticulated distinction between gauge theory and general relativity: the derivative order at which physical observables are associated with geometric objects.</p> <p>Although both frameworks are formulated in terms of connections and curvature, their assignment of physical meaning differs systematically. In gauge theory, curvature is directly identified with physical field strength, while observable effects such as phase shifts arise through line integrals of the connection. In general relativity, by contrast, force-like effects are governed by the connection itself, whereas curvature primarily encodes mass–energy distributions through the Einstein field equations.</p> <p>The present work does not propose modifications to established field equations, nor does it introduce new dynamical principles. Its contribution is interpretive and structural. By revisiting the historical development from Einstein to Yang–Mills, it makes explicit a derivative-order mismatch that remained implicit throughout twentieth-century field theory.</p> <p>The central claim is that line integrals and accumulated phase constitute a missing observational layer capable of accommodating both connection-based and curvature-based interpretations without conceptual tension. Once this layer is recognized, the mismatch ceases to appear problematic and instead emerges as a structural feature of how different theories organize local geometric data.</p> <p>Within this context, the 0-Sphere model is positioned not as a unification scheme, but as an explicit articulation of a line-integral-based observational framework that became historically available only after the maturation of gauge holonomy and gravitational time-dilation concepts.</p> <p>This document is archived to ensure transparency, continuity, and traceability within the ongoing 0-Sphere research program.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18809117 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | A Note on Derivative Hierarchy in Gauge Theory and Gravity: A Historical Supplement on Connection, Curvature, and Line-Integral Observables Hanamura, Satoshi <p>[41 Supplement]<br><br></p> <p>This supplementary note provides a historical and structural clarification of a largely unarticulated distinction between gauge theory and general relativity: the derivative order at which physical observables are associated with geometric objects.</p> <p>Although both frameworks are formulated in terms of connections and curvature, their assignment of physical meaning differs systematically. In gauge theory, curvature is directly identified with physical field strength, while observable effects such as phase shifts arise through line integrals of the connection. In general relativity, by contrast, force-like effects are governed by the connection itself, whereas curvature primarily encodes mass–energy distributions through the Einstein field equations.</p> <p>The present work does not propose modifications to established field equations, nor does it introduce new dynamical principles. Its contribution is interpretive and structural. By revisiting the historical development from Einstein to Yang–Mills, it makes explicit a derivative-order mismatch that remained implicit throughout twentieth-century field theory.</p> <p>The central claim is that line integrals and accumulated phase constitute a missing observational layer capable of accommodating both connection-based and curvature-based interpretations without conceptual tension. Once this layer is recognized, the mismatch ceases to appear problematic and instead emerges as a structural feature of how different theories organize local geometric data.</p> <p>Within this context, the 0-Sphere model is positioned not as a unification scheme, but as an explicit articulation of a line-integral-based observational framework that became historically available only after the maturation of gauge holonomy and gravitational time-dilation concepts.</p> <p>This document is archived to ensure transparency, continuity, and traceability within the ongoing 0-Sphere research program.</p> |
| title | A Note on Derivative Hierarchy in Gauge Theory and Gravity: A Historical Supplement on Connection, Curvature, and Line-Integral Observables |
| url | https://doi.org/10.5281/zenodo.18809117 |