Existence of atoms and molecules in non-relativistic quantum electrodynamics

Elliott H. Lieb, Michael Loss

Research output: Chapter in Book/Report/Conference proceedingChapter

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 α and for any value of the ultraviolet cutoff A on the radiation field. There is no infrared cutoff. The basic mathematical ingredient in our proof is a novel localization of 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.

Original languageEnglish (US)
Title of host publicationThe Stability of Matter
Subtitle of host publicationFrom Atoms to Stars: Fourth Edition
PublisherSpringer Berlin Heidelberg
Pages665-708
Number of pages44
ISBN (Print)3540420835, 9783540222125
DOIs
StatePublished - Jan 1 2005

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

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  • Cite this

    Lieb, E. H., & Loss, M. (2005). Existence of atoms and molecules in non-relativistic quantum electrodynamics. In The Stability of Matter: From Atoms to Stars: Fourth Edition (pp. 665-708). Springer Berlin Heidelberg. https://doi.org/10.1007/3-540-27056-6_42