Non-perturbative renormalization in Light Front Dynamics with Fock space truncation

TL;DR

This paper develops a non-perturbative renormalization scheme within Light-Front Dynamics using Fock space truncation, enabling analytical renormalization of QED's electric charge consistent with Ward Identity.

Contribution

It introduces a general non-perturbative renormalization method in Light-Front Dynamics that explicitly accounts for Fock space truncation and orientation dependence.

Findings

Successfully applied to QED with two-body truncation

Analytically reproduces electric charge renormalization

Ensures Ward Identity compliance

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 is essential in order to analyze the structure of the counterterms and bare parameters needed to renormalize the theory. We present here a general strategy to determine the dependence of these quantities on the Fock sectors. We apply our formalism to QED for the two-body (one fermion and one boson) truncation and recover analytically, without any perturbative expansion, the renormalization of the electric charge according to the requirements of the Ward Identity.