Manuscript X-E-ST@1 · X-E-ST.tex · section · 44614221

Definition and normalization

E4: the isolated matter-induced tree › Definition and normalization · lines 1370–1390

X-E-ST@1#eq:k1

The flat Wick stress tensor is

Θ^{μν} = : T_{0}^{μν} [ϕ] : .

Define the auxiliary retarded quadratic response

k_{1} [ϕ] = Δ_{gr}^{R} (\frac{1}{2} g Θ) = - 2 P_{tr} E_{0}^{R} (g Θ) .

It solves, in the distributional Wick sense,

P_{gr} k_{1} + \frac{δ V _{1, g}}{δ r} = 0

with retarded support. It is the scalar-sourced response used inside the observable, not a declaration of the full second-order interacting metric.

Displayed formulas in this passage

X-E-ST@1#eq:k1 · line 1377
$k_{1} [ϕ] = Δ_{gr}^{R} (\frac{1}{2} g Θ) = - 2 P_{tr} E_{0}^{R} (g Θ) .$
unlabeled · line 1373
$Θ^{μν} = : T_{0}^{μν} [ϕ] : .$
unlabeled · line 1384
$P_{gr} k_{1} + \frac{δ V _{1, g}}{δ r} = 0$