230 Appendix F: Heavy Quark Production Radiation Derivation in Fig. F.1. For t < 0 we close the contour in the upper half of the plane, picking up the k 0 = ⃗ k · ⃗ p/p 0 pole; the result is where the k 0 in the k 2 term is given by its value at the pole. Note that the 1 /p 0 comes from correctly evaluating the contour integral using Figure F.1: Pole structure of Eq. (F.34). A $^{µ}$( x ) = ∫ d $^{3}$k (2 π ) $_{3}$e i ⃗ k · ⃗ $^{x}$e − i ( ⃗ k · ⃗ p p 0 ) $_{t}$(2 πi ) 2 π − ie k 2 − p µ p 0 , (F.35) p µ k · p − iϵ = p µ k $^{0}$p0 − ⃗ k · ⃗ p − iϵ = p µ p 0   1 k 0 − ⃗ k · ⃗ p p 0 − iϵ$^{}$ $_{}$. (F.36) We can see that the k · p = 0 pole for t < 0 corresponds to the Coulomb field of the particle by boosting to its rest frame; we have that k 2 = −| ⃗ k | 2