Manuscript Em01-D@2 · Em01-D-v2.tex · section · d3b49151
Mathematical data versus physical identification
The designated contraction and its input conventions › Mathematical data versus physical identification · lines 355–428
Em01-D@2#eq:package
A mathematical input package consists of
Every entry is held fixed as .
The four crossed entries are distributions, with the component and relative-argument conventions printed below. The functions are fixed smooth functions; for the designated scalar root its identification is
with the designated advanced Klein–Gordon operator. The estimates proved here use the fixed smooth function , not an alternative choice of its propagator.
The source switch is smooth, with on , and is fixed. For the local analysis, observations and their derivatives are bounded on all compact sets used.
| Entry | Identification needed for a physical application |
|---|---|
| Metric cross-lines | Actual component distributions, tensor propagator factor, gauge, normalization, time ordering, boundary prescription, and any state-dependent smooth terms. |
| Scalar cross-lines | Actual mass-dependent distributions, state, normalization, boundary prescription, and relations to the selected Green operators. |
| Density map | An identification of the designated with a derivative or polarization of a specified quadratic density. |
| Source | The unintegrated cubic density, curvature convention, and propagated-output conversion of Section sec:source. |
| Observations and root | The frozen , the selected advanced root , and the source-switch assumptions; no diagnostic observation is substituted. |
| Corrections | The actual allowed correction space, extension reference, normalization conditions, and required output cone. |
The supplied materials do not provide a complete identification of the first three rows or the correction package. The theorem therefore applies to a fixed mathematical package (eq:package), and applies to the physical graph only after those identifications and its analytic certificate are proved.
Displayed formulas in this passage
Em01-D@2#eq:package · line 358
unlabeled · line 373