Manuscript X-D@3 · X-D-v3.tex · section · b7774529

VII-C's own signature and fixed model

VII-C checklist: copied hypotheses and failed match › VII-C's own signature and fixed model · lines 1137–1173

In this subsection only, VII-C uses

η_{VII} = diag (- 1, 1, 1, 1), □_{VII} = - \partial_{t}^{2} + Δ.

Its insertion is

B_{f} [h, ϕ] = - \int f w^{μ} [h] \partial_{μ} ϕ d^{4} x, w [h] = E_{0, VII} C_{VII} h,

with the sharp zero-Cauchy inverse and unrestricted smooth off-shell configurations.

Its Wick matrix includes a quantum graviton block

H_{hh α β ρ σ} = P_{α β ρ σ} Δ_{0}^{+}, P_{α β ρ σ} = η_{VII α (ρ} η_{VII σ) β} - \frac{1}{2} η_{VII α β} η_{VII ρ σ},

and a scalar block $H_{ϕϕ} = Δ_{m}^{+}$ , with zero cross blocks.

The signature dictionary is $η_{VII} = - η$ , $□_{VII} = - □$ , and $E_{0, VII} = - E_{0}$ for the same source. Raised-index formulas must be recomputed accordingly. This dictionary does not identify either the coordinate prescription or the quantum field content.

Displayed formulas in this passage

unlabeled · line 1140
$η_{VII} = diag (- 1, 1, 1, 1), □_{VII} = - \partial_{t}^{2} + Δ.$
unlabeled · line 1145
$B_{f} [h, ϕ] = - \int f w^{μ} [h] \partial_{μ} ϕ d^{4} x, w [h] = E_{0, VII} C_{VII} h,$
unlabeled · line 1154
$H_{hh α β ρ σ} = P_{α β ρ σ} Δ_{0}^{+}, P_{α β ρ σ} = η_{VII α (ρ} η_{VII σ) β} - \frac{1}{2} η_{VII α β} η_{VII ρ σ},$