Manuscript XVI-H@1 · XVI-H.tex · assumption · af895076

Assumption: Prepared source and quadratic bulk coefficient

Setting and inherited interfaces › Source premise · lines 379–414

XVI-H@1#input:source, XVI-H@1#eq:JD, XVI-H@1#eq:Dsig

The designated source is

J_{D} [γ] = σ J_{3} [γ] + D_{σ} [γ],

where

D_{σ}^{μν} = 2 C_{2}^{μν α β} \partial_{α} \partial_{β} σ - 2 M_{2}^{μν ρ} \partial_{ρ} σ .

The coefficient formulas are those displayed in Section sec:degree.

The bulk term $J_{3}$ is a finite local homogeneous quadratic differential polynomial in the metric jet, with coefficients independent of the perturbation. The total number of derivatives hitting its field factors is at most two. This is an imported premise, reported in XII-D as the quadratic coefficient

J_{3}^{μν} = 2 [κ^{2}] (- q_{κ} G^{μν} (q_{κ})), q_{κ} = η + κγ .

Its individual curvature monomials are not supplied or expanded in this note.

The full source has total field-derivative order at most two and vanishes for $t \leq 0$ as a polynomial in the field jet.

Displayed formulas in this passage

XVI-H@1#eq:JD · line 382
$J_{D} [γ] = σ J_{3} [γ] + D_{σ} [γ],$
XVI-H@1#eq:Dsig · line 388
$D_{σ}^{μν} = 2 C_{2}^{μν α β} \partial_{α} \partial_{β} σ - 2 M_{2}^{μν ρ} \partial_{ρ} σ .$
unlabeled · line 404
$J_{3}^{μν} = 2 [κ^{2}] (- q_{κ} G^{μν} (q_{κ})), q_{κ} = η + κγ .$

Nearby in this section

section: Source premise