Renormalization and dressing in quantum field theory

TL;DR

This paper demonstrates how renormalization techniques like dressing transformations and similarity renormalization can be applied in quantum field theory to obtain finite, accurate results for the S-matrix and bound states, removing divergences.

Contribution

It introduces a method combining dressing transformations and similarity renormalization to produce a finite dressed particle Hamiltonian in quantum field theory.

Findings

Dressed particle Hamiltonian is finite at all perturbation orders.

Accurate S-matrix and bound state energies are obtained.

Virtual particles are effectively removed from the theory.

Abstract

We illustrate the mass and charge renormalization procedures in quantum field theory using, as an example, a simple model of interacting electrons and photons. It is shown how addition of infinite renormalization counterterms to the Hamiltonian helps to obtain finite and accurate results for the S-matrix. In order to remove the ultraviolet divergences from the Hamiltonian, we apply the Greenberg-Schweber ``dressing transformation'' and the Glazek-Wilson ``similarity renormalization''. The resulting ``dressed particle'' Hamiltonian is finite in all orders of the perturbation theory and yields accurate S-matrix and bound state energies. The bare and virtual particles are removed from the theory, and physical dressed particles interact via direct action-at-a-distance.