$\int\limits_{\frac{1}{2} < ¦p¦ < 1} \frac{1}{p^2+r} \rightarrow \frac{1}{1+r}\int\limits_{\frac{1}{2} < ¦p¦ < 1} 1 $

$\int\limits_{\frac{1}{2} < ¦p¦ < 1} \frac{1}{p^2+r}\frac{1}{[(\frac{1}{2}q_1+\frac{1}{2}q_2-p)^2 +r]} \rightarrow \frac{1}{(1+r)^2}\int\limits_{\frac{1}{2} < ¦p¦ < 1} 1 $

Since the referenced document is behind a paywall, it is a little difficult to know for sure of the context, but when I see these two equations, it would appear they are making a simplification about the amplitudes associated with propagators (internal lines of Feynman diagrams). It appears to be saying the upper half of the range of values associate with momentum follow the rules of geometric progression or more appropriately a geometric series and the region of integration has a constant slope (e.g. there is a uniform accumulation in the identified region of integration) Represented as. $$ \int\limits_{\frac{1}{2} < ¦p¦ < 1} 1 $$

I would understand it as a statement about the behavior of the propagators at high momentum, e.g. they are well behaved, and the contribution of more complicated diagrams diminishes at higher orders.

Since the paper is Wilson's paper on renormalization, this interpretation would at least be consistent.

If anyone would like to further clarify, please do.

This post imported from StackExchange Physics at 2014-03-12 15:25 (UCT), posted by SE-user Hal Swyers