On higher order estimates in quantum electrodynamics

TL;DR

This paper introduces a novel method for deriving higher order estimates in quantum electrodynamics, simplifying the process especially for non-local semi-relativistic models, and extends previous results to new operators.

Contribution

The paper presents a new approach that avoids iterated commutator expansions and applies it to both existing and new non-local quantum electrodynamics operators.

Findings

Re-derivation of earlier higher order estimates

New estimates for non-local molecular no-pair operator

Simplified method for semi-relativistic models

Abstract

We propose a new method to derive certain higher order estimates in quantum electrodynamics. Our method is particularly convenient in the application to the non-local semi-relativistic models of quantum electrodynamics as it avoids the use of iterated commutator expansions. We re-derive higher order estimates obtained earlier by Fr\"ohlich, Griesemer, and Schlein and prove new estimates for a non-local molecular no-pair operator.