Planar Matrices and Arrays of Feynman Diagrams

Understand

Very recently planar collections of Feynman diagrams were proposed by Borges and one of the authors as the natural generalization of Feynman diagrams for the computation of $k=3$ biadjoint amplitudes.

• Planar collections are one-dimensional arrays of metric trees satisfying an induced planarity and compatibility condition.
• In this work we introduce planar matrices of Feynman diagrams as the objects that compute $k=4$ biadjoint amplitudes.
• These are symmetric matrices of metric trees satisfying compatibility conditions.