{"acknowledgement":"We are grateful to Elliott Lieb for helpful discussions. C.H. was supported by a Marie Curie Fellowship of the European Community programme “Improving Human Research Potential and the Socioeconomic Knowledge Base” under contract number HPMFCT-2000-00660 and by the Deutsche Forschungsgemeinschaft, and acknowledges kind hospitality at Princeton University, where part of this work was done. R.S. was supported by the Austrian Science Fund in the form of an Erwin Schrödinger Fellowship.\r\n","volume":6,"publist_id":"4574","intvolume":"         6","year":"2002","citation":{"mla":"Hainzl, Christian, and Robert Seiringer. “Mass Renormalization and Energy Level Shift in Non-Relativistic QED.” <i>Advances in Theoretical and Mathematical Physics</i>, vol. 6, no. 5, International Press, 2002, pp. 847–71, doi:<a href=\"https://doi.org/10.4310/ATMP.2002.v6.n5.a3\">10.4310/ATMP.2002.v6.n5.a3</a>.","ieee":"C. Hainzl and R. Seiringer, “Mass renormalization and energy level shift in non-relativistic QED,” <i>Advances in Theoretical and Mathematical Physics</i>, vol. 6, no. 5. International Press, pp. 847–871, 2002.","ista":"Hainzl C, Seiringer R. 2002. Mass renormalization and energy level shift in non-relativistic QED. Advances in Theoretical and Mathematical Physics. 6(5), 847–871.","chicago":"Hainzl, Christian, and Robert Seiringer. “Mass Renormalization and Energy Level Shift in Non-Relativistic QED.” <i>Advances in Theoretical and Mathematical Physics</i>. International Press, 2002. <a href=\"https://doi.org/10.4310/ATMP.2002.v6.n5.a3\">https://doi.org/10.4310/ATMP.2002.v6.n5.a3</a>.","apa":"Hainzl, C., &#38; Seiringer, R. (2002). Mass renormalization and energy level shift in non-relativistic QED. <i>Advances in Theoretical and Mathematical Physics</i>. International Press. <a href=\"https://doi.org/10.4310/ATMP.2002.v6.n5.a3\">https://doi.org/10.4310/ATMP.2002.v6.n5.a3</a>","ama":"Hainzl C, Seiringer R. Mass renormalization and energy level shift in non-relativistic QED. <i>Advances in Theoretical and Mathematical Physics</i>. 2002;6(5):847-871. doi:<a href=\"https://doi.org/10.4310/ATMP.2002.v6.n5.a3\">10.4310/ATMP.2002.v6.n5.a3</a>","short":"C. Hainzl, R. Seiringer, Advances in Theoretical and Mathematical Physics 6 (2002) 847–871."},"article_type":"original","_id":"2350","language":[{"iso":"eng"}],"publication":"Advances in Theoretical and Mathematical Physics","author":[{"first_name":"Christian","last_name":"Hainzl","full_name":"Hainzl, Christian"},{"orcid":"0000-0002-6781-0521","full_name":"Seiringer, Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","last_name":"Seiringer","first_name":"Robert"}],"page":"847 - 871","doi":"10.4310/ATMP.2002.v6.n5.a3","publication_identifier":{"issn":["1095-0761"]},"external_id":{"arxiv":["math-ph/0205044v3"]},"status":"public","quality_controlled":"1","title":"Mass renormalization and energy level shift in non-relativistic QED","date_created":"2018-12-11T11:57:09Z","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","oa_version":"Published Version","oa":1,"scopus_import":"1","publisher":"International Press","issue":"5","date_published":"2002-09-01T00:00:00Z","publication_status":"published","extern":"1","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/math-ph/0205044"}],"abstract":[{"text":"Using the Pauli-Fierz model of non-relativistic quantum electrodynamics, we calculate the binding energy of an electron in the field of a nucleus of charge Z and in presence of the quantized radiation field. We consider the case of small coupling constant α, but fixed Zα and ultraviolet cut-off Λ. We prove that after renormalizing the mass the binding energy has, to leading order in α, a finite limit as Λ goes to infinity; i.e., the cut-off can be removed. The expression for the ground state energy shift thus obtained agrees with Bethe's formula for small values of Zα, but shows a different behavior for bigger values.","lang":"eng"}],"day":"01","type":"journal_article","date_updated":"2023-07-26T08:29:28Z","month":"09","article_processing_charge":"No"}