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 $H=-g{\psi }^2(x)\varphi (x)$, we calculate nonperturbatively the renormalized state vector of a scalar "nucleon" in a truncated Fock space containing the $N$, $N\pi$ and $N\pi \pi$ sectors. The model gives a simple example of non-perturbative renormalization which is carried out numerically. Though the mass renormalization $\delta m^2$ diverges logarithmically with the cutoff $L$, the Fock components of the "physical" nucleon are stable when $L\to \infty$.

22 pages, 5 figures

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