Non-perturbative approach in truncated Fock space including antifermion

Non-perturbative approach which we develop is based on representation of the state vector as a set of Fock components. After truncation to a finite number of components, we come to a coupled-channel problem which is solved non-perturbatively, in light-front dynamics, without using any decomposition in degrees of the coupling constant. Previously [J.-F. Mathiot, V.A. Karmanov and A.V. Smirnov, Proc. of Sci., LC2008:024, 2008; arXiv:0812.1100[hep-ph].], in Yukawa model, we took into account the Fock sectors corresponding to single fermion, a fermion coupled to one boson, and a fermion coupled to two bosons. Now we extend the Fock space and incorporate also the fermion-antifermion pair, i.e., the Fock sector with two fermions and one antifermion. An appropriate non-perturbative renormalization procedure is developed.