content_image/308801.jpg content_image/308803.jpg content_image/308804.jpg
in Fig. F.1. 

<img src='content_image/308801.jpg'>

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 

<img src='content_image/308803.jpg'>

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 

<img src='content_image/308804.jpg'>

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 

