Existence of atoms and molecules in non-relativistic quantum electrodynamics

Elliott H. Lieb, Michael Loss

Research output: Contribution to journalArticle

47 Scopus citations

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 Λ 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)
Pages (from-to)667-710
Number of pages44
JournalAdvances in Theoretical and Mathematical Physics
Volume7
Issue number4
DOIs
StatePublished - Jul 2003

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Physics and Astronomy(all)

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