Stability of Ultraviolet-Cutoff¶Quantum Electrodynamics with Non-Relativistic Matter

We prove that the quantum-mechanical ground state energy of a system consisting of an arbitrary number, M, of static nuclei of atomic number ≤Z and of an arbitrary number, N, of Pauli electrons interacting with the quantized, ultraviolet-cutoff radiation field is bounded below by $-K.M, where K is a finite constant depending on Z, on the finestructure constant α and on the ultraviolet cutoff Λ, with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document}, as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document}, and K' independent of Λ.