Manuscript IV@1 · IV.tex · section · 351cb2d7

Transfer variables and the time factor

Model 2: spectral removal at fixed number cutoff › Transfer variables and the time factor · lines 1711–1729

Set $ℓ = T - t_{0}$ , $γ = (2 π)^{- 3}$ , and define

F (s, k) = \int v_{f} (t_{0} + s, x) e^{ik \cdot x} d x, J (k, ν) = \int_{0}^{ℓ} F (s, k) e^{- i ν s} d s .

The four uncut legs are

H^{++} H^{+-} H^{-+} H^{--} = G (p, q) J (p + q, ∣ p ∣ + E_{q}), = G (p, q) J (p - q, ∣ p ∣ - E_{q}), = G (p, q) J (- p + q, - ∣ p ∣ + E_{q}), = G (p, q) J (- p - q, - ∣ p ∣ - E_{q}),

where

G (p, q) = γ \frac{Π ( p ) ( q \otimes q )}{∣ p ∣ E _{q}} .

Displayed formulas in this passage

unlabeled · line 1719
$H^{++} H^{+-} H^{-+} H^{--} = G (p, q) J (p + q, ∣ p ∣ + E_{q}), = G (p, q) J (p - q, ∣ p ∣ - E_{q}), = G (p, q) J (- p + q, - ∣ p ∣ + E_{q}), = G (p, q) J (- p - q, - ∣ p ∣ - E_{q}),$
unlabeled · line 1714
$F (s, k) = \int v_{f} (t_{0} + s, x) e^{ik \cdot x} d x, J (k, ν) = \int_{0}^{ℓ} F (s, k) e^{- i ν s} d s .$
unlabeled · line 1726
$G (p, q) = γ \frac{Π ( p ) ( q \otimes q )}{∣ p ∣ E _{q}} .$