Abstract
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 -algebra. The recursion relation is obtained in the transition to a smallest representative in the quasi-isomorphism class of that -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.
- Received 25 March 2019
DOI:https://doi.org/10.1103/PhysRevD.100.045017
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Published by the American Physical Society