WKB approximation to loop diagrams

Question

I'm a bit confused with the terminology here.

This paper claimed to use WKB method to calculate the usual loop diagrams. Notice that the vertex is approximated by expanding around the classical (on-shell) solution of the massive particle propagator. However this method doesn't look like the usual WKB I know. AFAIK in WKB (eikonal) approximation we are supposed to expand the propagator around the particle limit of the solution, but NOT the classical field limit.

So, how do you describe the WKB method in QFT? Is it practical enough to give us quick intuitive calculation on our system?

(probably in this sense, the WKB+1loop is the crudest semiclassical approximation we can do -> first order in $\hbar$ and coupling constant)

Answer 1

Damn, it took me a while to notice what 'eikonal' really means in the paper's context (which is also true in general).

Since the gluon is soft, its wavelength is much larger than the wavelength of the quarks. This means the gluon sees the quarks as particles.

Alternatively, I can view the gluon as a 'slowly varying background field', which is the condition for WKB. So this is basically a WKB method in momentum space.