Antiparticle Contribution in the Cross Ladder Diagram for Two Boson Propagation in the Light-front

In the light-front milieu, there is an implicit assumption that the vacuum is trivial. By this " triviality " is meant that the Fock space of solutions for equations of motion is sectorized in two, one of positive energy k- and the other of negative one corresponding respectively to positive and negative momentum k+. It is assumed that only one of the Fock space sector is enough to give a complete description of the solutions, but in this work we consider an example where we demonstrate that both sectors are necessary.