QFT method for indefinite Kac-Moody Theory: A step towards classification

We propose a quantum field theory (QFT) method to approach the classification of indefinite sector of Kac-Moody algebras. In this approach, Vinberg relations are interpreted as the discrete version of the QFT_{2} equation of motion of a scalar field and Dynkin diagrams as QFT_{2} Feynman graphs. In particular, we show that Dynkin diagrams of su(n+1) series (n\geq 1) can be interpreted as free field propagators and T_{p,q,r} diagrams as the vertex of \phi^{3} interaction. Other results are also given.