Systematic renormalization scheme in light-front dynamics with Fock space truncation

TL;DR

This paper develops a non-perturbative renormalization scheme within light-front dynamics, utilizing Fock space truncation, and demonstrates its application to Yukawa, QED, and scalar models, successfully recovering charge renormalization.

Contribution

It introduces a Fock space truncation-based renormalization method in light-front dynamics, accounting for sector-dependent counterterms and parameters, with explicit dependence on light-front orientation.

Findings

Successfully applied to two- and three-body truncations in various models.

Recovered QED charge renormalization without perturbation theory.

Provided a general strategy for calculating state vectors in truncated Fock space.

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 counterterms and bare parameters needed to renormalize the theory depend on the Fock sectors. We present a general strategy in order to calculate these quantities, as well as state vectors of physical systems, in a truncated Fock space. The explicit dependence of our formalism on the orientation of the light front plane is essential in order to analyze the structure of the counterterms. We apply our formalism to the two-body (one fermion and one boson) truncation in the Yukawa model and in QED, and to the three-body truncation in a scalar model. In QED, we recover analytically, without any perturbative expansion, the renormalization of the electric charge, according to the requirements of the Ward identity.