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Front. Phys.    2012, Vol. 7 Issue (5) : 533-575    https://doi.org/10.1007/s11467-012-0270-z
REVIEW ARTICLE
An introduction to on-shell recursion relations
Bo Feng1,2, Mingxing Luo1()
1. Zhejiang Institute of Modern Physics,Zhejiang University, Hangzhou 310027, China; 2. Center of Mathematical Science, ZhejiangUniversity, Hangzhou 310027, China
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Abstract

This article provides an introduction to on-shell recursionrelations for calculations of tree-level amplitudes. Starting withthe basics, such as spinor notations and color decompositions, weexpose analytic properties of gauge-boson amplitudes, BCFW-deformations,the large z-behavior of amplitudes, and on-shell recursion relationsof gluons. We discuss further developments of on-shell recursion relations,including generalization to other quantum field theories, supersymmetrictheories in particular, recursion relations for off-shell currents,recursion relation with nonzero boundary contributions, bonus relations,relations for rational parts of one-loop amplitudes, recursion relationsin 3D and a proof of CSW rules. Finally, we present samples of applications,including solutions of split helicity amplitudes and of N = 4 SYM theories, consequences of consistentconditions under recursion relation, Kleiss-Kuijf (KK) and Bern-Carrasco-Johansson(BCJ) relations for color-ordered gluon tree amplitudes, Kawai-Lewellen-Tye(KLT) relations.
Keywords amplitude      on-shell recursionrelation     
Corresponding Author(s): Luo Mingxing,Email:mingxingluo@zju.edu.cn   
Issue Date: 01 October 2012
 Cite this article:   
Bo Feng,Mingxing Luo. An introduction to on-shell recursion relations[J]. Front. Phys. , 2012, 7(5): 533-575.
 URL:  
https://academic.hep.com.cn/fop/EN/10.1007/s11467-012-0270-z
https://academic.hep.com.cn/fop/EN/Y2012/V7/I5/533
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