Manuscript XIII-D@1 · XIII-D.tex · section · bab69024

The assembled coefficient and unchanged action

Copied prerequisite sheet › The assembled coefficient and unchanged action · lines 413–445

XIII-D@1#eq:O, XIII-D@1#eq:slots

The displayed lift is

O = Φ^{(2)}_{D} + A_{1} [f, g] (r_{g} [ϕ]; ϕ), Φ^{(2)}_{D} = A_{2}^{sc} [f, g] (γ, 0; ϕ) - C_{3, D},

with

r_{D} = P E_{0}^{R} J_{D} = - u_{D}, r_{g} [ϕ] = - \frac{1}{2} P E_{0}^{R} (g T_{0} [ϕ]) .

The opposite insertion sign is already detected and is not reopened XIIE.

The action is XII-C's cubic-only density weighting,

S_{grav, D} = S_{EH} + κ \int (σ_{ε} - 1) ℓ_{3} d^{4} x .

Its fixed-input jet $J_{g, σ}^{D} (ϕ_{m}) = \emptyset$ is retained as a boundary, not an interaction entry XIIC. The inverse coefficient remains $- 1$ . The free rule $s_{0} γ = R c$ is odd and has ghost number one; it is not the even rule $Y_{ξ}$ studied here XIIA,XIB.

Displayed formulas in this passage

XIII-D@1#eq:O · line 416
$O = Φ^{(2)}_{D} + A_{1} [f, g] (r_{g} [ϕ]; ϕ), Φ^{(2)}_{D} = A_{2}^{sc} [f, g] (γ, 0; ϕ) - C_{3, D},$
XIII-D@1#eq:slots · line 424
$r_{D} = P E_{0}^{R} J_{D} = - u_{D}, r_{g} [ϕ] = - \frac{1}{2} P E_{0}^{R} (g T_{0} [ϕ]) .$
unlabeled · line 434
$S_{grav, D} = S_{EH} + κ \int (σ_{ε} - 1) ℓ_{3} d^{4} x .$