content_image/324447.jpg content_image/324448.jpg content_image/324449.jpg content_image/324450.jpg content_image/324451.jpg content_image/324455.jpg
With this normalization for the transforms we have that 

Solving the EOM (Eq. (F.24)) in momentum space we find that 

<img src='content_image/324447.jpg'>

<img src='content_image/324448.jpg'>

<img src='content_image/324449.jpg'>

We can find ˜ j from the given trajectory (Eq. (F.26)) and the definition of the Fourier transform: 

<img src='content_image/324450.jpg'>

<img src='content_image/324451.jpg'>

Therefore we have the field in position space as an integral over momentum: 

<img src='content_image/324455.jpg'>

The integral on the right hand side (RHS) has the pole structure as shown 

