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

Christian Hainzl, Masao Hirokawa, Herbert Spohn

研究成果: ジャーナルへの寄稿学術誌査読

17 被引用数 (Scopus)

抄録

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 Ebin =me4Z2/8π2 to leading order in e. We investigate the radiative corrections to the binding energy and prove upper and lower bounds which imply that Ebin=me4 Z2/8π2 + c0e6 O(e7 ln e) with explicit coefficient c0 and independent of the ultraviolet cutoff. c0 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.

本文言語英語
ページ(範囲)424-459
ページ数36
ジャーナルJournal of Functional Analysis
220
2
DOI
出版ステータス出版済み - 3月 15 2005
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