A bound on binding energies and mass renormalization in models of quantum electrodynamics

Elliott H. Lieb, Michael Loss

Research output: Contribution to journalArticle

24 Scopus citations

Abstract

We study three models of matter coupled to the ultraviolet cutoff, quantized radiation field and to the Coulomb potential of arbitrarily many nuclei. Two are nonrelativistic: the first uses the kinetic energy (p+eA(x))2 and the second uses the Pauli-Fierz energy (p+eA(x)) 2+eσ·B(x). The third, no-pair model, is relativistic and replaces the kinetic energy with the Dirac operator D(A), but restricted to its positive spectral subspace, which is the "electron subspace." In each case we are able to give an upper bound to the binding energy as distinct from the less difficult ground state energy. This implies, for the first time we believe, an estimate, albeit a crude one, of the mass renormalization in these theories.

Original languageEnglish (US)
Pages (from-to)1057-1069
Number of pages13
JournalJournal of Statistical Physics
Volume108
Issue number5-6
DOIs
StatePublished - Dec 1 2002

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Keywords

  • Mass renormalization
  • Quantum electrodynamics

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