According to page 101 of *Scattering Amplitudes* (Elvang, Huang), one can use the zone variables $y$ to define a unique integrand, in the planar case.

This is done by saying that the momenta associated to an internal line is $y_a - y_b$ where $y_a$ and $y_b$ are the zone variable associated to the two zones adjacent to the particular line.

In this scheme, is it necessary to also devise a scheme to canonically label the interior zone variables, in order to obtain a well-defined integrand function?

To clarify, if one considers a double box integral, and swaps the two zone variables associated to the internal faces, one obtains two different contributions to the integrand. In fact, there will be two internal lines whose propagators are $(y_4 - y_a)^{-2} (y_2 - y_b)^{-2}$ which is not the same function if one swaps $a$ with $b$.

This post imported from StackExchange Physics at 2015-12-05 17:38 (UTC), posted by SE-user giulio bullsaver