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

Reduced form factors

The once-subtracted retarded prescription › Reduced form factors · lines 698–724

XVIII-B@2#eq:referencePi

Define the retarded boundary value by analytic continuation from $Im p^{0} > 0$ :

F_{i}^{R} (p) = F_{i} ((p^{0} + i 0)^{2} - ∣ p ∣^{2}) .

On real momenta this is $F_{i} (p^{2} + i 0 sgn p^{0})$ at the spectral cut. The advanced value reverses the sign.

The reference response is

Π_{ref, ab c d}^{R} (p) = ℏ [(Q_{2})_{ab c d} (p) F_{2}^{R} (p) + (Q_{0})_{ab c d} (p) F_{0}^{R} (p)] .

The tensor structures in this formula are polynomials on all momenta; there is no singular projector evaluation at $p^{2} = 0$ .

Displayed formulas in this passage

XVIII-B@2#eq:referencePi · line 712
$Π_{ref, ab c d}^{R} (p) = ℏ [(Q_{2})_{ab c d} (p) F_{2}^{R} (p) + (Q_{0})_{ab c d} (p) F_{0}^{R} (p)] .$
unlabeled · line 702
$F_{i}^{R} (p) = F_{i} ((p^{0} + i 0)^{2} - ∣ p ∣^{2}) .$