Nonperturbative renormalization in a scalar model within light-front dynamics

Abstract

Within the covariant formulation of light-front dynamics, in a scalar model with the interaction Hamiltonian $H=\ensuremath{-}g{\ensuremath{\psi}}^{2}(x)\ensuremath{\varphi}(x),$ we calculate nonperturbatively the renormalized state vector of a scalar ``nucleon'' in a truncated Fock space containing the N, $N\ensuremath{\pi}$ and $N\ensuremath{\pi}\ensuremath{\pi}$ sectors. The model gives a simple example of nonperturbative renormalization that is carried out numerically. Though the mass renormalization $\ensuremath{\delta}{m}^{2}$ diverges logarithmically with increasing cutoff L, the Fock components of the ``physical'' nucleon are stable when $\stackrel{\ensuremath{\rightarrow}}{L}\ensuremath{\infty}.$