Manuscript X-G@1 · X-G.tex · section · 01566e14

The ordinary two-vertex fish

The local fish and the nonlocal product criterion › The ordinary two-vertex fish · lines 1487–1505

X-G@1#eq:fish

Let $D_{F}^{μ}$ denote flat scalar Feynman product data and

D_{F}^{gr} = - 4 P D_{F}^{0} .

The metric–scalar fish between two matter vertices has finite sums of component kernels of the form

t_{α β} (r) = D_{F}^{0} (r) \partial^{α} \partial^{β} D_{F}^{m} (r), ∣ α ∣ + ∣ β ∣ \leq 2, r \neq = 0.

Tensor coefficients and external scalar derivatives are suppressed.

Displayed formulas in this passage

X-G@1#eq:fish · line 1495
$t_{α β} (r) = D_{F}^{0} (r) \partial^{α} \partial^{β} D_{F}^{m} (r), ∣ α ∣ + ∣ β ∣ \leq 2, r \neq = 0.$
unlabeled · line 1490
$D_{F}^{gr} = - 4 P D_{F}^{0} .$