Manuscript XVIII-B@2 · XVIII-B-v2.tex · section · 27ed4f4b

Reduced form factors

The once-subtracted retarded prescription › Reduced form factors · lines 650–665

XVIII-B@2#eq:subtracted

For $i \in {2, 0}$ and $z \in C ∖ [a, \infty)$ , define

F_{i} (z) = \int_{a}^{\infty} r_{i} (u) (\frac{1}{u - z} - \frac{1}{u}) d u = z \int_{a}^{\infty} \frac{r _{i} ( u )}{u ( u - z )} d u .

The subtraction is in the reduced form factor. It is not a once-subtracted integral of the growing projector density $ρ_{i} = u^{2} r_{i}$ .

Displayed formulas in this passage

XVIII-B@2#eq:subtracted · line 653
$F_{i} (z) = \int_{a}^{\infty} r_{i} (u) (\frac{1}{u - z} - \frac{1}{u}) d u = z \int_{a}^{\infty} \frac{r _{i} ( u )}{u ( u - z )} d u .$