Bound States in Minkowski Space in 2 + 1 Dimensions

Abstract

The Nakanishi perturbative integral representation of the Bethe–Salpeter amplitude in three-dimensions (2 + 1) is used to solve the corresponding homogeneous Bethe–Salpeter equation in Minkowski space. The projection of this equation onto the null-plane, as reported here, leads to a bound-state equation for the Nakanishi weight function. The explicit forms of the integral equation for the Nakanishi weight function are shown in the ladder approximation. In addition, the valence light-front wave function is presented. The formal steps of the formalism are illustrated to some extend, with the resulting equation being applied to a bound state system composed by two identical scalar particles of mass m, interacting through the exchange of another massive scalar particle of mass μ. The results reported in this contribution show quite good agreement between our calculations obtained from the Bethe–Salpeter amplitude with the Nakanishi weight function with direct solutions obtained in the Euclidean space.