Nonperturbative renormalization in light-front dynamics and applications

TL;DR

This paper develops a nonperturbative, covariant light-front dynamics framework for calculating properties of relativistic systems, with applications to QED, scalar systems, and the Yukawa model, ensuring controlled convergence and renormalization.

Contribution

It introduces a systematic, nonperturbative renormalization scheme within covariant light-front dynamics applicable to various models and truncations, improving convergence control and rotational invariance handling.

Findings

Reproduces the Schwinger electron magnetic moment in two-body truncation.

Analyzes scalar systems with antiparticle effects in three-body approximation.

Calculates fermion structure in the Yukawa model with three-body truncation.

Abstract

We present a general framework to calculate the properties of relativistic compound systems from the knowledge of an elementary Hamiltonian. Our framework provides a well-controlled nonperturbative calculational scheme which can be systematically improved. The state vector of a physical system is calculated in light-front dynamics. From the general properties of this form of dynamics, the state vector can be further decomposed in well-defined Fock components. In order to control the convergence of this expansion, we advocate the use of the covariant formulation of light-front dynamics. In this formulation, the state vector is projected on an arbitrary light-front plane $\omega \cd x=0$ defined by a light-like four-vector $\omega$. This enables us to control any violation of rotational invariance due to the truncation of the Fock expansion. We then present a general nonperturbative renormalization scheme in order to avoid field-theoretical divergences which may remain uncancelled due to this truncation. This general framework has been applied to a large variety of models. As a starting point, we consider QED for the two-body Fock space truncation and calculate the anomalous magnetic moment of the electron. We show that it coincides, in this approximation, with the well-known Schwinger term. Then we investigate the properties of a purely scalar system in the three-body approximation, where we highlight the role of antiparticle degrees of freedom. As a non-trivial example of our framework, we calculate the structure of a physical fermion in the Yukawa model, for the three-body Fock space truncation (but still without antifermion contributions). We finally show why our approach is also well-suited to describe effective field theories like chiral perturbation theory in the baryonic sector.