Variational Backbone and Regime Closures III: Conservative & Semiclassical Closure Density-fixed Laplace backbone and the R3 corridor: KG-type principal part, exact KG→Sch identity, NR/WKB gates, and semiclassical HJ locking
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| Format: | Recurso digital |
| Langue: | anglais |
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2025
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| _version_ | 1866901868011061248 |
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| author | Yi, Yunbeom |
| author_facet | Yi, Yunbeom |
| contents | <p>We close the R3 (conservative / time-completed) regime at the level of principal<br>symbols under the series rule that the spatial density e(·) is held fixed across readings. The<br>contribution is not a claim of deriving “all physics” from the full functional E[g, IR, II ] in one<br>step, but a corridor-level closure: once the open-sector Laplace-type backbone is fixed by<br>the density-fixed rule, and one adopts standard conservative completion/correspondence gates,<br>a rigid chain follows.<br>Concretely, (i) any local linear second-order time completion preserving the Laplace back-<br>bone yields a Klein–Gordon-type principal part; (ii) a rest-mass phase rotation gives an exact<br>KG→Sch identity with explicit relativistic correction; (iii) under a quantitative slow-envelope<br>gate ε = ℏω/(mc2) ≪ 1 on a fixed time window, the identity reduces to Schr¨odinger dynamics;<br>(iv) in the local-potential presentation, WKB yields exact continuity/phase equations and for-<br>mally reduces to Hamilton–Jacobi as ℏ → 0. As a design constraint in the series, within a<br>fixed linear scalar, local, second-order Laplace-type Schr¨odinger class (up to lower-order pertur-<br>bations, possibly order-0 operators), the semiclassical kinetic term is locked to be quadratic;<br>“HJ-only modification” is excluded unless the operator class is changed.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18036834 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Variational Backbone and Regime Closures III: Conservative & Semiclassical Closure Density-fixed Laplace backbone and the R3 corridor: KG-type principal part, exact KG→Sch identity, NR/WKB gates, and semiclassical HJ locking Yi, Yunbeom Physics Theoretical Physics High Energy Physics – Theory Informational Projection Theory Gauge symmetry Abelian and non-Abelian gauge theory Yang–Mills theory Noether currents Informational currents Open and closed information Informational curvature Fifth force Long-range interactions Fundamental interactions Quantum gravity Cosmology Black hole physics Information conservation <p>We close the R3 (conservative / time-completed) regime at the level of principal<br>symbols under the series rule that the spatial density e(·) is held fixed across readings. The<br>contribution is not a claim of deriving “all physics” from the full functional E[g, IR, II ] in one<br>step, but a corridor-level closure: once the open-sector Laplace-type backbone is fixed by<br>the density-fixed rule, and one adopts standard conservative completion/correspondence gates,<br>a rigid chain follows.<br>Concretely, (i) any local linear second-order time completion preserving the Laplace back-<br>bone yields a Klein–Gordon-type principal part; (ii) a rest-mass phase rotation gives an exact<br>KG→Sch identity with explicit relativistic correction; (iii) under a quantitative slow-envelope<br>gate ε = ℏω/(mc2) ≪ 1 on a fixed time window, the identity reduces to Schr¨odinger dynamics;<br>(iv) in the local-potential presentation, WKB yields exact continuity/phase equations and for-<br>mally reduces to Hamilton–Jacobi as ℏ → 0. As a design constraint in the series, within a<br>fixed linear scalar, local, second-order Laplace-type Schr¨odinger class (up to lower-order pertur-<br>bations, possibly order-0 operators), the semiclassical kinetic term is locked to be quadratic;<br>“HJ-only modification” is excluded unless the operator class is changed.</p> |
| title | Variational Backbone and Regime Closures III: Conservative & Semiclassical Closure Density-fixed Laplace backbone and the R3 corridor: KG-type principal part, exact KG→Sch identity, NR/WKB gates, and semiclassical HJ locking |
| topic | Physics Theoretical Physics High Energy Physics – Theory Informational Projection Theory Gauge symmetry Abelian and non-Abelian gauge theory Yang–Mills theory Noether currents Informational currents Open and closed information Informational curvature Fifth force Long-range interactions Fundamental interactions Quantum gravity Cosmology Black hole physics Information conservation |
| url | https://doi.org/10.5281/zenodo.18036834 |