Existence of Atoms and Molecules in Non-Relativistic Quantum Electrodynamics

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.

LaTex file, 40 pages, errors and misprints corrected and references added. This paper will appear in ATMP (Advances in Theoretical and Mathematical Physics)