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arXiv · 1903.05713

Scattering Amplitude Recursion Relations in BV Quantisable Theories

Tommaso Macrelli·Christian Saemann·Martin Wolf
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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 MHV amplitudes. We show that the origin of this recursion relation becomes clear in the BV formalism, which encodes a field theory in an $L_\infty$-algebra. The recursion relation is obtained in the transition to a smallest representative in the quasi-isomorphism class of that $L_\infty$-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 quantisable theory, which, in turn, produces recursion relations for its tree-level scattering amplitudes.

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Tommaso Macrelli, Christian Saemann, Martin Wolf. 2020-10-21. Scattering Amplitude Recursion Relations in BV Quantisable Theories. https://doi.org/10.1103/physrevd.100.045017

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