Scattering Amplitude Recursion Relations in BV Quantisable Theories

Understand

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.