Manuscript XIII-E@1 · XIII-E.tex · section · 74eaba48

The unchanged sheet

E0: the pair, carrier, order, and contact class › The unchanged sheet · lines 411–444

XIII-E@1#eq:carrier

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}, 0 < ε < T .

The functions $g \in C_{c}^{\infty} (M_{T}^{\circ}; [0, 1])$ and $σ_{ε}$ are fixed backgrounds. All fields are ambient smooth multiplets. No decay assumption is added.

The carrier is

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

There is no quotient by $N_{W}$ .

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

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

No Einstein–Hilbert interaction vertex is inserted into the selected pair XIIC.

Displayed formulas in this passage

XIII-E@1#eq:carrier · line 429
$E_{H} = (F_{mc, pol} [[ℏ, κ]], ⋆_{H}) / N_{sol} [[ℏ, κ]] .$
unlabeled · line 414
$M = R^{4}, η = diag (1, - 1, - 1, - 1), □ = \partial_{t}^{2} - Δ_{x}, P_{m} = □ + m^{2},$
unlabeled · line 420
$M_{T} = [0, T] \times R^{3}, M_{T}^{\circ} = (0, T) \times R^{3}, 0 < ε < T .$
unlabeled · line 438
$S_{grav, D} = S_{EH} + κ \int (σ_{ε} - 1) ℓ_{3} d^{4} x .$