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Binding energy for hydrogen-like atoms in the Nelson model without cutoffs

Authors
Journal
Journal of Functional Analysis
0022-1236
Publisher
Elsevier
Publication Date
Volume
220
Issue
2
Identifiers
DOI: 10.1016/j.jfa.2004.07.009
Keywords
  • Nonrelativistic Qed
  • Perturbative Bounds
Disciplines
  • Physics

Abstract

Abstract In the Nelson model particles interact through a scalar massless field. For hydrogen-like atoms there is a nucleus of infinite mass and charge Ze, Z > 0 , fixed at the origin and an electron of mass m and charge e. This system forms a bound state with binding energy E bin = me 4 Z 2 / 8 π 2 to leading order in e. We investigate the radiative corrections to the binding energy and prove upper and lower bounds which imply that E bin = me 4 Z 2 / 8 π 2 + c 0 e 6 + O ( e 7 ln e ) with explicit coefficient c 0 and independent of the ultraviolet cutoff. c 0 can be computed by perturbation theory, which however is only formal since for the Nelson Hamiltonian the smallest eigenvalue sits exactly at the bottom of the continuous spectrum.

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