Effects of the virtual particle number on theSmatrix of the (φ4)1+1model

We present results of the S matrix in the (${\phi }^4$ ${)}_{1+1}$ model obtained by a nonperturbative calculation using a momentum-space discretization technique. First, we calculate the two-body S matrix in the strong-coupling regime (up to ${\lambda }_{\mathrm{eff}=3\mathrm{}}$), with the restriction of taking into account only two-body virtual particle states. We find agreement with standard perturbation theory obtained by summing up the corresponding graphs to infinite order. We also estimate the effect of mass renormalization. Second, we investigate the effect of including higher virtual particle numbers in two-particle scattering in the cases ${\lambda }_{\mathrm{eff}=(1/6)\mathrm{}}$ and ${\lambda }_{\mathrm{eff}=1\mathrm{}}$. In both cases we find convergence of the S matrix with respect to increasing the virtual-particle-number cutoff.