Nonperturbative renormalization in a scalar model within Light-Front Dynamics

TL;DR

This paper demonstrates a nonperturbative renormalization approach within Light-Front Dynamics for a scalar model, showing stable physical states despite divergences in mass renormalization.

Contribution

It provides a numerical nonperturbative renormalization method in Light-Front Dynamics for a scalar model with Fock space truncation, illustrating stability of physical states.

Findings

Mass renormalization diverges logarithmically with cutoff.

Fock components of the physical nucleon remain stable as cutoff increases.

Numerical implementation of nonperturbative renormalization in Light-Front Dynamics.

Abstract

Within the covariant formulation of Light-Front Dynamics, in a scalar model with the interaction Hamiltonian $H=-g\psi^{2}(x)\phi(x)$, 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 $L\to\infty$.