Renormalized nonperturbative fermion model in Covariant Light Front Dynamics

TL;DR

This paper develops a nonperturbative renormalization scheme for fermion models in Covariant Light-Front Dynamics, analyzing gauge dependence and rotational invariance restoration, with analytical solutions for various gauge choices.

Contribution

It introduces a novel nonperturbative renormalization approach in Covariant Light-Front Dynamics, including gauge-specific counterterms and analysis of rotational invariance restoration.

Findings

Analytical fermion state vectors and counterterms for spinless and gauge bosons.

Extra counterterm needed for rotational invariance in Light-Front Dynamics.

Solutions in Feynman and Light-Cone gauges are equivalent up to normalization.

Abstract

Within the framework of the covariant formulation of Light-Front Dynamics, we develop a nonperturbative renormalization scheme in the fermion model supposing that the composite fermion is a superposition of the "bare" fermion and a fermion+boson state. We first assume the constituent boson to be spinless. Then we address the case of gauge bosons in the Feynman and in the Light-Cone gauges. For all these cases the fermion state vector and the necessary renormalization counterterms are calculated analytically. It turns out that in Light-Front Dynamics, to restore the rotational invariance, an extra counterterm is needed, having no any analogue in Feynman approach. For gauge bosons the results obtained in the two gauges are compared with each other. In general, the number of spin components of the two-body (fermion+boson) wave function depends on the gauge. But due to the two-body Fock space truncation, only one non-zero component survives for each gauge. And moreover, the whole solutions for the state vector, found for the Feynman and Light-Cone gauges, are the same (except for the normalization factor). The counterterms are however different