Journal of High Energy Physics

, 2019:10 | Cite as

L-algebras and the perturbiner expansion

  • Cristhiam Lopez-ArcosEmail author
  • Alexander Quintero Vélez
Open Access
Regular Article - Theoretical Physics


Certain classical field theories admit a formal multi-particle solution, known as the perturbiner expansion, that serves as a generating function for all the tree-level scattering amplitudes and the Berends-Giele recursion relations they satisfy. In this paper it is argued that the minimal model for the L-algebra that governs a classical field theory contains enough information to determine the perturbiner expansion associated to such theory. This gives a prescription for computing the tree-level scattering amplitudes by inserting the perturbiner solution into the homotopy Maurer-Cartan action for the L-algebra. We confirm the method in the non-trivial examples of bi-adjoint scalar and Yang-Mills theories.


Scattering Amplitudes Differential and Algebraic Geometry BRST Quantization 


Open Access

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Grupo de Electrónica y Automatización, Institución universitaria Salazar y HerreraMedellínColombia
  2. 2.Escuela de MatemáticasUniversidad Nacional de Colombia Sede MedellínMedellínColombia

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