Tree-Level Formalism

Abstract

We review two novel techniques used to calculate tree-level scattering amplitudes efficiently: MHV diagrams, and on-shell recursion relations. For the MHV diagrams, we consider applications to tree-level amplitudes and focus in particular on the N=4 supersymmetric formulation. We also briefly describe the derivation of loop amplitudes using MHV diagrams. For the recursion relations, after presenting their general proof, we discuss several applications to massless theories with and without supersymmetry, to theories with massive particles, and to graviton amplitudes in General Relativity. This article is an invited review for a special issue of Journal of Physics A devoted to "Scattering Amplitudes in Gauge Theories".

40 pages, 8 figures, invited review for a special issue of Journal of Physics A devoted to "Scattering Amplitudes in Gauge Theories", R. Roiban(ed), M. Spradlin(ed), A. Volovich(ed); v2: minor corrections, references added

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Cited by in corpus (20)

• Basics of Generalized Unitarity
• Harmony of Super Form Factors
• Scattering Amplitudes and Wilson Loops in Twistor Space
• Scattering amplitudes: the most perfect microscopic structures in the universe
• An Introduction to On-shell Recursion Relations
• Susy Theories and QCD: Numerical Approaches
• The Multi-Regge limit of NMHV Amplitudes in N=4 SYM Theory
• New structures in scattering amplitudes: a review
• Exact Superconformal and Yangian Symmetry of Scattering Amplitudes
• SUSY Ward identities, Superamplitudes, and Counterterms
• Twistor-strings and gravity tree amplitudes
• Symbols of One-Loop Integrals From Mixed Tate Motives
• Integrability and MHV diagrams in N=4 supersymmetric Yang-Mills theory
• Tree-level amplitudes and dual superconformal symmetry
• Holonomies of gauge fields in twistor space 4: functional MHV rules and one-loop amplitudes
• Perturbative Methods for Superconformal Quantum Field Theories in String - Gauge Theory Dualities
• Deconstructing Supersymmetric S-matrices in D <= 2 + 1
• Hidden Local and Non-local Symmetries of S-matrices of N=2,4,8 SYM in D=2+1
• Cachazo-Svrcek-Witten Rules for Tree-Level Gluonic Amplitudes Revisited
• A Celestial Description of Planar Super-Yang-Mills Theory