Scattering amplitudes in YM and GR as minimal model brackets and their recursive characterization

Understand

Attached to both Yang-Mills and General Relativity about Minkowski spacetime are distinguished gauge independent objects known as the on-shell tree scattering amplitudes.

• We reinterpret and rigorously construct them as $L_\infty$ minimal model brackets.
• This is based on formulating YM and GR as differential graded Lie algebras.
• Their minimal model brackets are then given by a sum of trivalent (cubic) Feynman tree graphs.