Manuscript XIV-H@1 · XIV-H.tex · input · 695c7c3a

Input statement: XII-E and XII-C

H0: copied handoffs and their domains › Earlier handoffs · lines 572–609

XIV-H@1#input:EC, XIV-H@1#eq:actualsource

The response and first-completion formulas are

r_{D} = P E_{0}^{R} J_{D}, X^{μ} [r] = - E_{0}^{R} \partial_{α} (σ_{ε} a_{1}^{α μ} [r]),

p [r; ψ] = - E_{m}^{R} (V_{1, g} [r] ψ),

a_{1}^{μν} [r] = \frac{1}{2} η^{μν} tr_{η} r - r^{μν}, b_{1} [r] = \frac{1}{2} tr_{η} r .

The existing completion kernels are tree kernels XIIE.

The actual source is

J_{D} = EL_{γ} (σ_{ε} ℓ_{3}) = σ_{ε} J_{3} + D_{σ}_{ε}, D_{σ}_{ε}^{μν} = 2 C_{2}^{μν α β} \partial_{α} \partial_{β} σ_{ε} - 2 M_{2}^{μν ρ} \partial_{ρ} σ_{ε} .

Its fixed unintegrated cubic representative is

ℓ_{3} [γ] = - 2 [ρ^{3}] (- det (η + ρ γ) R [η + ρ γ]) .

The selected weighting is at cubic order only XIIC.

Displayed formulas in this passage

XIV-H@1#eq:actualsource · line 591
$J_{D} = EL_{γ} (σ_{ε} ℓ_{3}) = σ_{ε} J_{3} + D_{σ}_{ε}, D_{σ}_{ε}^{μν} = 2 C_{2}^{μν α β} \partial_{α} \partial_{β} σ_{ε} - 2 M_{2}^{μν ρ} \partial_{ρ} σ_{ε} .$
unlabeled · line 575
$r_{D} = P E_{0}^{R} J_{D}, X^{μ} [r] = - E_{0}^{R} \partial_{α} (σ_{ε} a_{1}^{α μ} [r]),$
unlabeled · line 579
$p [r; ψ] = - E_{m}^{R} (V_{1, g} [r] ψ),$
unlabeled · line 582
$a_{1}^{μν} [r] = \frac{1}{2} η^{μν} tr_{η} r - r^{μν}, b_{1} [r] = \frac{1}{2} tr_{η} r .$
unlabeled · line 602
$ℓ_{3} [γ] = - 2 [ρ^{3}] (- det (η + ρ γ) R [η + ρ γ]) .$