Manuscript XVIII-B@2 · XVIII-B-v2.tex · section · 27ed4f4b
Frozen data and the selected response
Frozen data and the selected response · lines 286–332
The double integral in (eq:response) is distributional. The function is compact and smooth; no pointwise multiplication of singular kernels is being used.
. The selected connected source-degree-two coefficient consists of the two Wick contractions between the two normal-ordered stress insertions, together with its completely classified local extension freedom.
| Contribution | Status in this target |
|---|---|
| Two scalar lines between the two stress insertions | Included, with both identical-particle contractions. |
| Vacuum disconnected one-point factors | Zero by the specified Wick ordering. |
| Finite transverse local contacts | Included and classified in Theorem thm:contacts. |
| Graviton loops and graviton external quantum legs | Absent: the source is classical. |
| Ghost and auxiliary-field contributions | Absent: no gravitational gauge-fixed quantum theory is specified. |
| Nonlinear metric seagulls | Outside the model: the coupling is defined to be linear. |
| Relational coordinate and scalar completion insertions | Outside the model: the insertion is (eq:stress). |
| Higher source cumulants | Outside the quadratic-order claim. |
The distinction between a two-stress correlator and the full second variation of a metric-dependent action, including local variation terms, is important in the external linear-response literature AMP,Mottola. Those works motivate a comparison; they do not insert seagulls into the present linear-source definition.