Ladder Bethe-Salpeter equation on the Light-Front

Antiparticle Contribution in the Cross Ladder Diagram for Bethe-Salpeter Equation in the Light-Front

“…Truncate now G (3) to order g 2 and G (4) up to g 0 , including in this way, the intermediate propagations of three and four bodies in the kernel of the integral equation for G…”

“…Also, recently, the Bethe-Salpeter equation in the "ladder" approximation has been solved in Minkowski space [3]. However up to the time of the publication of J.H.O.Sales work [4,5] there was no detailed comparison between the results in the four dimensional calculations and in the light front, with the kernel including the propagation of intermediate states of four bodies. The objective was to study the effect of the components of the Fock space with particle number greater than three, going beyond the previously done works in the area.…”

Light-front time picture of few-body systems

“…0 (K)vg (4) 0 (K)vg (3) (K); which goes beyond the quasipotential expansion in second order, where, instead of g (3) (K), one has g…”

“…The BSE is equivalent to an infinite set of coupled equations for Green's functions with different number of particles, which also allows a consistent truncation of the light-front Fock-space. This set of coupled equations comes from a quasi-potential expansion of the BSE on the light-front [2][3][4]. The relative light-front time between the particles is eliminated in favor of a global time.…”

Solving the Bethe–Salpeter Equation in Euclidean Space

“…[13], and a reduction of the BS equation to an equation of the Light Front form has been proposed in Ref. [9]. Moreover, a detailed investigation of the solution and the properties of two spinor particle in a bound state within Light Front Dynamics have been reported in Refs.…”