Non-perturbative Renormalization in Truncated Yukawa Model

An approach to non-perturbative calculations in the light-front quantum field theory and its new developments are briefly reviewed. We start with the decomposition of the state vector in Fock components. After truncation of this decomposition (main approximation in this approach), the eigenvalue equation for the light-front Hamiltonian generates, in Minkowski space, a finite system of integral equations for the Fock components. Solving this system numerically and performing the non-perturbative renormalization, we find the state vector of fermion in the quenched scalar Yukawa model, up to the four-body truncation (one fermion + three bosons), for rather large values of the coupling constant. With the state vector, found in this way, the fermion electromagnetic form factors are calculated. Comparing results obtained in the four-body truncation with those found in the previous, three-body truncation, we discover very good convergence relative to truncation, that indicates that we are close to the exact non-perturbative solution in this field-theoretical model. The approach can be extended to more realistic field theories and, after further development, it could constitute an alternative to the lattice calculations.