Manuscript XIV-E@1 · XIV-E.tex · section · e89fd2a5

Geometry and product data

E0: the six-branch contract › Geometry and product data · lines 448–491

Use

M = R^{4}, η = diag (1, - 1, - 1, - 1), □ = \partial_{t}^{2} - Δ_{x}, P_{m} = □ + m^{2},

M_{T} = [0, T] \times R^{3}, M_{T}^{\circ} = (0, T) \times R^{3} .

All external data remain those fixed in XIV-C and XIV-D. No observation, switch, or width is chosen after a symbol calculation.

The carrier remains

E_{H} = (F_{mc, pol} [[ℏ, κ]], ⋆_{H}) / N_{sol} [[ℏ, κ]] .

The frozen time-ordered line is

H_{T} = H + i G_{act}^{A} .

Metric–scalar blocks vanish. The numerical species factors and the inverse coefficient $- 1$ are unchanged.

The interaction is

V_{g} = - \frac{1}{2} \int g γ_{μν} T_{0}^{μν} [ϕ] d^{4} x,

where

T_{0}^{μν} [ϕ] = \partial^{μ} ϕ \partial^{ν} ϕ - \frac{1}{2} η^{μν} ((\partial ϕ)^{2} - m^{2} ϕ^{2}) .

The scalar-sourced slot of $O$ is included once. It is not removed because its scalar–scalar channel vanishes on the retained output-location patch.

Displayed formulas in this passage

unlabeled · line 451
$M = R^{4}, η = diag (1, - 1, - 1, - 1), □ = \partial_{t}^{2} - Δ_{x}, P_{m} = □ + m^{2},$
unlabeled · line 457
$M_{T} = [0, T] \times R^{3}, M_{T}^{\circ} = (0, T) \times R^{3} .$
unlabeled · line 464
$E_{H} = (F_{mc, pol} [[ℏ, κ]], ⋆_{H}) / N_{sol} [[ℏ, κ]] .$
unlabeled · line 470
$H_{T} = H + i G_{act}^{A} .$
unlabeled · line 477
$V_{g} = - \frac{1}{2} \int g γ_{μν} T_{0}^{μν} [ϕ] d^{4} x,$
unlabeled · line 482
$T_{0}^{μν} [ϕ] = \partial^{μ} ϕ \partial^{ν} ϕ - \frac{1}{2} η^{μν} ((\partial ϕ)^{2} - m^{2} ϕ^{2}) .$