Scattering amplitude recursion relations in Batalin-Vilkovisky-quantizable theories

Tommaso Macrelli, Christian Saemann, Martin Wolf

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Tree-level scattering amplitudes in Yang-Mills theory satisfy a recursion relation due to Berends and Giele which yields e.g., the famous Parke-Taylor formula for maximally helicity violating amplitudes. We show that the origin of this recursion relation becomes clear in the Batalin-Vilkovisky (BV) formalism, which encodes a field theory in an L∞-algebra. The recursion relation is obtained in the transition to a smallest representative in the quasi-isomorphism class of that L∞-algebra, known as a minimal model. In fact, the quasi-isomorphism contains all the information about the scattering theory. As we explain, the computation of such a minimal model is readily performed in any BV quantizable theory, which, in turn, produces recursion relations for its tree-level scattering amplitudes.

Original languageEnglish
Article number045017
JournalPhysical Review D
Issue number4
Publication statusPublished - 16 Aug 2019

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)


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