Jacobian conjecture: coloring Abdesselam-Rivasseau model

Abstract

We consider the Abdesselam-Rivasseau (AR) model turning the Jacobian Conjecture (JC) into a problem of the perturbative quantum field theory. Within the AR model, the JC inverse map is represented by a formal integral generating the tree's expansion for this map. By assigning colors to the edges in the vertex of the AR model and performing selective Gaussian integration, we show the termination of the tree's series for the inverse map. The latter implies the correctness of JC.