Amplitudes in YM and GR as a Minimal Model and Recursive Characterization

Abstract We study the tree scattering amplitudes of Yang–Mills and General Relativity as functions complex momenta, using a homological geometrical approach. This approach uses differential graded Lie algebras, one for YM GR, whose Maurer Cartan equations are classical field equations. The obtained $$L_\infty $$ L ∞ minimal model brackets, given by trivalent Feynman expansion. show that they sections sheaf on variety their residues factor in characteristic way. requires classifying irreducible codimension subvarieties where poles occur; constructing dedicated gauges make factorization manifest; proving flexible version gauge independence to be able work with different gauges. residue yields simple recursive characterization exploiting Hartogs’ phenomenon singular varieties. is similar inspired Britto–Cachazo–Feng–Witten recursion, but avoids BCFW’s trick shifting hence conditions at infinity under such shifts.