# Relativistic model of Hamiltonian renormalization for bound states and scattering amplitudes

## TL;DR

This paper applies the renormalization group procedure for effective particles to a simplified fermion-scalar Yukawa model, demonstrating the method's steps in a truncated Fock space framework.

## Contribution

It introduces a simplified fermion-scalar model to test the RGPEP in Hamiltonian dynamics, providing analytic insights into the renormalization process.

## Key findings

- Successful application of RGPEP to a truncated Yukawa model
- Analytic demonstration of renormalization steps in Hamiltonian dynamics
- Insights into bound states and scattering amplitudes within the model

## Abstract

We test the renormalization group procedure for effective particles (RGPEP) on a model of fermion-scalar interaction based on the Yukawa theory. The model is obtained by truncating the Yukawa theory to just two Fock sectors in the Dirac front form of Hamiltonian dynamics, a fermion, and a fermion and a boson, for the purpose of simple analytic calculation that exhibits steps of the procedure.