Non-Perturbative Mass and Charge Renormalization in Relativistic No-Photon Quantum Electrodynamics

TL;DR

This paper develops a non-perturbative, cut-off free renormalized Hamiltonian for relativistic no-photon QED, enabling a rigorous analysis of the Lamb shift in muonic atoms.

Contribution

It introduces a novel non-perturbative renormalization method for the Hamiltonian in no-photon QED, extending the mathematical rigor of quantum electrodynamics.

Findings

Well-defined restriction to the one-electron subspace

Non-perturbative, cut-off free construction of the Hamiltonian

Relevance for Lamb shift in muonic atoms

Abstract

Starting from a formal Hamiltonian as found in the physics literature -- omitting photons -- we define a renormalized Hamiltonian through charge and mass renormalization. We show that the restriction to the one-electron subspace is well-defined. Our construction is non-perturbative and does not use a cut-off. The Hamiltonian is relevant for the description of the Lamb shift in muonic atoms.