# I BCFW recursion relation

1. Nov 23, 2016

### Lapidus

Below is a snipet from http://file:///C:/Users/Christian.Hollersen/Downloads/Britto_2011_2%20(1).pdf [Broken] of Britto. Similar explanation can be found in the QFT books of Zee, Schwarz or the Scattering Amplitude text of Huang. Or any other text that covers BCFW recursion. My dumb question: how and why does the residue at this pole take this funny factorization form? (For clarifcation: residue is the just the word QFT people use for the numerator of a rational function with a simple pole, right?)

Thank you!

Last edited by a moderator: May 8, 2017
2. Nov 25, 2016

### OldManAndTheSeaQuark

There are at least two ways to show the factorization of amplitudes on simple poles. An ancient proof using only properties of the S-matirx (analyticity, unitarity and cluster decomposition) can be found in Eden et al. "The Analytic S-matrix" sec. 4.5. For a more recent discussion see the nice review by Conde

http://pos.sissa.it/archive/conferences/201/005/Modave 2013_005.pdf

Alternatively there is a more local field theoretic proof given in Weinberg "The Quantum Theory of Fields Vol 1." sec. 10.2.