Renormalized non-perturbative scalar and fermions models in Covariant Light Front Dynamics

TL;DR

This paper develops a non-perturbative renormalization scheme within Covariant Light-Front Dynamics, using Fock space truncation and analyzing counterterms for scalar and fermion models.

Contribution

It introduces a formalism that explicitly accounts for light-front orientation dependence to systematically renormalize scalar and fermion models non-perturbatively.

Findings

Successful application to scalar models

Extension to fermion models demonstrated

Framework clarifies counterterm structure

Abstract

Within the framework of the Covariant formulation of Light-Front Dynamics, we develop a general non-perturbative renormalization scheme, based on the Fock decomposition of the state vector and its truncation. The explicit dependence of our formalism on the orientation of the light front, defined by a light-like four vector $\omega$, is essential in order to analyze the structure of the counterterms needed to renormalize the theory. We illustrate our framework for scalar and fermion models