Ab initio nonperturbative calculation of physical observables in light-front dynamics. Application to the Yukawa model

TL;DR

This paper introduces a nonperturbative method for calculating physical observables in light-front dynamics, applying it to the Yukawa model to demonstrate scale-independent form factors and extending the approach to include antifermion effects.

Contribution

It presents a novel nonperturbative strategy using Fock space decomposition and covariant light-front dynamics, with a Fock sector dependent renormalization scheme, applied to the Yukawa model.

Findings

Form factors are independent of the regularization scale at large scales.

The approach successfully handles three-body Fock space truncation.

Including antifermion degrees of freedom extends the model's applicability.

Abstract

We present a coherent and operational strategy to calculate, in a nonperturbative way, physical observables in light-front dynamics. This strategy is based on the decomposition of the state vector of any compound system in Fock components, and on the covariant formulation of light-front dynamics, together with the so-called Fock sector dependent renormalization scheme. We apply our approach to the calculation of the electromagnetic form factors of a fermion in the Yukawa model, in the nontrivial three-body Fock space truncation, for rather large values of the coupling constant. We find that, once the renormalization conditions are properly taken into account, the form factors do not depend on the regularization scale, when the latter is much larger than the physical masses. We then extend the Fock space by including antifermion degrees of freedom.