content_image/296399.jpg content_image/296398.jpg content_image/296397.jpg content_image/296396.jpg content_image/296395.jpg content_image/296394.jpg
with the other momenta the same, is 

<img src='content_image/296399.jpg'>

## F.3.3 Massive Charge and Massless Field with Recoil 

In the case of a massless field the QFT and classical results are necessarily the same; we have 

<img src='content_image/296398.jpg'>

Everything is consistent with taking m$_{γ}$ → 0 from our previous result. Again we see the overall factor of (1 − x ) 2 out front. We’re tempted to simply take M$_{Q}$ → 0 to recover the completely massless limit. However in the massless limit we must actually solve a completely different problem: for a massless charge we cannot take it to be at rest for t < 0. Perhaps of anecdotal interest the totally massless with recoil bremsstrahlung result, using 

is 

this is clearly not what we are interested in. 

<img src='content_image/296397.jpg'>

<img src='content_image/296396.jpg'>

<img src='content_image/296395.jpg'>

<img src='content_image/296394.jpg'>

