4th order similarity renormalization of a model hamiltonian

TL;DR

This paper investigates a fourth-order similarity renormalization scheme for a fermion-boson Hamiltonian, showing it maintains covariance and reproduces known solutions, thus advancing systematic renormalization methods.

Contribution

It demonstrates how to choose counterterms in the similarity renormalization scheme to preserve covariance and reproduce established solutions up to fourth order.

Findings

Covariance of the T-matrix is maintained up to fourth order.

Eigenvalue equations reduce to the Dirac equation for physical fermions.

Reproduces the G{}azek and Perry model solution.

Abstract

We study the similarity renormalization scheme for hamiltonians to the fourth order in perturbation theory using a model hamiltonian for fermions coupled to bosons. We demonstrate that the free finite parts of counterterms can be chosen in such a way that the T-matrix is covariant up to the fourth order and the eigenvalue equation for the physical fermion reduces to the Dirac equation. Through this choice, the systematic renormalization scheme reproduces the model solution originally proposed by G{\l}azek and Perry.