Existence of Atoms and Molecules in Non-Relativistic Quantum Electrodynamics

TL;DR

This paper proves the existence of ground states for a quantum system of electrons, nuclei, and radiation under certain conditions, using a novel electromagnetic field localization technique.

Contribution

It introduces a new localization method for the electromagnetic field that enables proving ground state existence without infrared cutoff in non-relativistic QED.

Findings

Ground state exists for N < Z+1 electrons and nuclei.

Result holds for any fine structure constant and ultraviolet cutoff.

No infrared cutoff needed for the proof.

Abstract

We show that the Hamiltonian describing N nonrelativistic electrons with spin, interacting with the quantized radiation field and several fixed nuclei with total charge Z has a ground state when N <Z+1. The result holds for any value of the fine structure constant alpha and for any value of the ultraviolet cutoff Lambda on the radiation field. There is no infrared cutoff. The basic mathematical ingredient in our proof is a novel way of localizing the electromagnetic field in such a way that the errors in the energy are of smaller order than 1/L, where L is the localization radius.