BCFW recursion

{{Short description|Set of recursion relations in quantum field theory}}

The Britto–Cachazo–Feng–Witten recursion relations are a set of on-shell recursion relations in quantum field theory.{{cite web|url=http://testweb.science.uu.nl/ITF/teaching/2012/Brecht%20Truijen.pdf |title=Britto-Cachazo-Feng-Witten Recursion: An Introduction |author=Brecht Truijen |date=August 2012 |accessdate=23 September 2013 |url-status=dead |archiveurl=https://web.archive.org/web/20140221230929/http://testweb.science.uu.nl/ITF/teaching/2012/Brecht%20Truijen.pdf |archivedate=21 February 2014 }}{{cite web|url=http://theory.fnal.gov/seminars/slides/2006/ALazopoulos.pdf|title=B.C.F.W. Recursion Relations and the Link to Feynman Graphs|author=Achilleas Lazopoulos|date=24 August 2006|accessdate=23 September 2013|archive-url=https://web.archive.org/web/20130927131408/http://theory.fnal.gov/seminars/slides/2006/ALazopoulos.pdf|archive-date=27 September 2013|url-status=dead}} They are named for their creators, Ruth Britto, Freddy Cachazo, Bo Feng and Edward Witten.

The BCFW recursion method is a way of calculating scattering amplitudes.{{cite journal|author1=Ruth Britto|author2=Freddy Cachazo|author3=Bo Feng|author4=Edward Witten|title=Direct Proof of Tree-Level Recursion Relation in Yang-Mills Theory|doi=10.1103/PhysRevLett.94.181602|year=2005|journal=Physical Review Letters|volume=94|issue=18|arxiv=hep-th/0501052|bibcode = 2005PhRvL..94r1602B|pmid=15904356|page=181602|s2cid=10180346 }} This technique is widely used in analytic calculations{{cite journal|arxiv=1111.5759|author1=Bo Feng|author2=Mingxing Luo|title=An Introduction to On-shell Recursion Relations|year=2011|doi=10.1007/s11467-012-0270-z|volume=7|issue=5|journal=Frontiers of Physics|pages=533–575|bibcode = 2012FrPhy...7..533F |s2cid=118409551 }} due to the relative conciseness of the resulting expressions, when compared to the more traditional methods. The principal property of the BCFW recursion is that at every stage of the calculation it involves exclusively real (on-shell) particles, as opposed to the virtual (off-shell) particles that propagate inside conventional Feynman diagrams.