content_image/327420.jpg content_image/327421.jpg content_image/327422.jpg content_image/327425.jpg
For a conserved current, ∂$_{β}$j β = 0, we have a consistency equation 

Our EOM, Eq. (F.61), become 

Fourier analysis immediately leads one to 

<img src='content_image/327420.jpg'>

<img src='content_image/327421.jpg'>

<img src='content_image/327422.jpg'>

The poles in this occur at k · p ′ = 0, k · p = 0, and k 2 − µ 2 = 0; the pole structure is exactly the same as for the massless case, Fig. F.1, but with the radiation poles giving a dispersion relation of 

<img src='content_image/327425.jpg'>

Let’s examine the t < 0 case and make sure we recover the correct Yukawa 

