  Within the covariant formulation of light-front dynamics, we calculate the
state vector of a fermion coupled to identical scalar bosons (the Yukawa
model). The state vector is decomposed in Fock sectors and we consider the
first three ones: a single fermion, a fermion coupled to one boson, and a
fermion coupled to two bosons. This last three-body sector generates nontrivial
and nonperturbative contributions to the state vector, and these contributions
are calculated with no approximations. The divergences of the amplitudes are
regularized using Pauli-Villars fermion and boson fields. Physical observables
can be unambiguously deduced using a systematic renormalization scheme we
developed. This renormalization scheme is a necessary condition in order to
avoid uncancelled divergences when Fock space is truncated. As an example, we
present preliminary numerical results for the anomalous magnetic moment of a
fermion in the Yukawa model.
