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

Simple item page
dc.creatorHainzl, Christian
dc.creatorHirokawa, Masao
dc.creatorSpohn, Herbert
dc.date2003-12-10
dc.date.accessioned2026-07-07T04:30:48Z
dc.date.available2026-07-07T04:30:48Z
dc.descriptionIn 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 $E_{\rm bin} = me^4Z^2/2$ to leading order in $e$. We investigate the radiative corrections to the binding energy and prove upper and lower bounds which imply that $ E_{\rm bin} = me^4 Z^2/2 + c_0 e^6 + \Ow(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.
dc.description30 pages, AMSLatex
dc.identifierhttps://arxiv.org/abs/math-ph/0312025
dc.identifierhttp://arxiv.org/abs/math-ph/0312025
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/57593
dc.subjectMathematical Physics
dc.titleBinding energy for hydrogen-like atoms in the Nelson model without cutoffs
dc.typetext

Files

Collections

arXiv