[{"month":"09","publist_id":"4574","status":"public","language":[{"iso":"eng"}],"extern":"1","type":"journal_article","date_published":"2002-09-01T00:00:00Z","external_id":{"arxiv":["math-ph/0205044v3"]},"publisher":"International Press","issue":"5","quality_controlled":"1","page":"847 - 871","day":"01","date_updated":"2023-07-26T08:29:28Z","publication":"Advances in Theoretical and Mathematical Physics","arxiv":1,"intvolume":"         6","volume":6,"oa":1,"author":[{"first_name":"Christian","last_name":"Hainzl","full_name":"Hainzl, Christian"},{"full_name":"Seiringer, Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","last_name":"Seiringer","first_name":"Robert"}],"user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","date_created":"2018-12-11T11:57:09Z","_id":"2350","citation":{"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.","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.","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>","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>.","short":"C. Hainzl, R. Seiringer, Advances in Theoretical and Mathematical Physics 6 (2002) 847–871.","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>","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>."},"year":"2002","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"}],"publication_status":"published","title":"Mass renormalization and energy level shift in non-relativistic QED","article_processing_charge":"No","oa_version":"Published Version","scopus_import":"1","doi":"10.4310/ATMP.2002.v6.n5.a3","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/math-ph/0205044"}],"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","publication_identifier":{"issn":["1095-0761"]},"article_type":"original"},{"date_updated":"2023-05-16T12:12:41Z","publication":"Advances in Theoretical and Mathematical Physics","intvolume":"         5","arxiv":1,"volume":5,"oa":1,"user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","author":[{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","first_name":"László","last_name":"Erdös"},{"first_name":"Horng","last_name":"Yau","full_name":"Yau, Horng"}],"date_created":"2018-12-11T11:59:20Z","_id":"2736","abstract":[{"lang":"eng","text":"We consider the time evolution of N bosonic particles interacting via a mean field Coulomb potential. Suppose the initial state is a product wavefunction. We show that at any finite time the correlation functions factorize in the limit N → ∞. Furthermore, the limiting one particle density matrix satisfies the nonlinear Hartree equation. The key ingredients are the uniqueness of the BBGKY hierarchy for the correlation functions and a new apriori estimate for the many-body Schrödinger equations."}],"citation":{"ieee":"L. Erdös and H. Yau, “Derivation of the nonlinear Schrödinger equation from a many body Coulomb system,” <i>Advances in Theoretical and Mathematical Physics</i>, vol. 5, no. 6. International Press, pp. 1169–1205, 2001.","ista":"Erdös L, Yau H. 2001. Derivation of the nonlinear Schrödinger equation from a many body Coulomb system. Advances in Theoretical and Mathematical Physics. 5(6), 1169–1205.","ama":"Erdös L, Yau H. Derivation of the nonlinear Schrödinger equation from a many body Coulomb system. <i>Advances in Theoretical and Mathematical Physics</i>. 2001;5(6):1169-1205. doi:<a href=\"https://doi.org/10.48550/arXiv.math-ph/0111042\">10.48550/arXiv.math-ph/0111042</a>","mla":"Erdös, László, and Horng Yau. “Derivation of the Nonlinear Schrödinger Equation from a Many Body Coulomb System.” <i>Advances in Theoretical and Mathematical Physics</i>, vol. 5, no. 6, International Press, 2001, pp. 1169–205, doi:<a href=\"https://doi.org/10.48550/arXiv.math-ph/0111042\">10.48550/arXiv.math-ph/0111042</a>.","chicago":"Erdös, László, and Horng Yau. “Derivation of the Nonlinear Schrödinger Equation from a Many Body Coulomb System.” <i>Advances in Theoretical and Mathematical Physics</i>. International Press, 2001. <a href=\"https://doi.org/10.48550/arXiv.math-ph/0111042\">https://doi.org/10.48550/arXiv.math-ph/0111042</a>.","apa":"Erdös, L., &#38; Yau, H. (2001). Derivation of the nonlinear Schrödinger equation from a many body Coulomb system. <i>Advances in Theoretical and Mathematical Physics</i>. International Press. <a href=\"https://doi.org/10.48550/arXiv.math-ph/0111042\">https://doi.org/10.48550/arXiv.math-ph/0111042</a>","short":"L. Erdös, H. Yau, Advances in Theoretical and Mathematical Physics 5 (2001) 1169–1205."},"year":"2001","oa_version":"Published Version","article_processing_charge":"No","publication_status":"published","title":"Derivation of the nonlinear Schrödinger equation from a many body Coulomb system","publication_identifier":{"issn":["1095-0761"]},"article_type":"original","scopus_import":"1","doi":"10.48550/arXiv.math-ph/0111042","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/math-ph/0111042"}],"publist_id":"4156","status":"public","month":"11","extern":"1","language":[{"iso":"eng"}],"type":"journal_article","external_id":{"arxiv":["math-ph/0111042"]},"date_published":"2001-11-01T00:00:00Z","publisher":"International Press","issue":"6","quality_controlled":"1","day":"01","page":"1169 - 1205"},{"language":[{"iso":"eng"}],"extern":"1","month":"09","publist_id":"5747","status":"public","publisher":"International Press","type":"journal_article","external_id":{"arxiv":["math/9805071"]},"date_published":"1998-09-01T00:00:00Z","issue":"5","page":"1011 - 1040","day":"01","quality_controlled":"1","arxiv":1,"intvolume":"         2","date_updated":"2022-09-01T14:09:49Z","publication":"Advances in Theoretical and Mathematical Physics","author":[{"first_name":"Tamas","last_name":"Hausel","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","full_name":"Hausel, Tamas"}],"user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","volume":2,"oa":1,"citation":{"ieee":"T. Hausel, “Vanishing of intersection numbers on the moduli space of Higgs bundles,” <i>Advances in Theoretical and Mathematical Physics</i>, vol. 2, no. 5. International Press, pp. 1011–1040, 1998.","ista":"Hausel T. 1998. Vanishing of intersection numbers on the moduli space of Higgs bundles. Advances in Theoretical and Mathematical Physics. 2(5), 1011–1040.","ama":"Hausel T. Vanishing of intersection numbers on the moduli space of Higgs bundles. <i>Advances in Theoretical and Mathematical Physics</i>. 1998;2(5):1011-1040. doi:<a href=\"https://doi.org/10.4310/ATMP.1998.v2.n5.a3\">10.4310/ATMP.1998.v2.n5.a3</a>","mla":"Hausel, Tamás. “Vanishing of Intersection Numbers on the Moduli Space of Higgs Bundles.” <i>Advances in Theoretical and Mathematical Physics</i>, vol. 2, no. 5, International Press, 1998, pp. 1011–40, doi:<a href=\"https://doi.org/10.4310/ATMP.1998.v2.n5.a3\">10.4310/ATMP.1998.v2.n5.a3</a>.","short":"T. Hausel, Advances in Theoretical and Mathematical Physics 2 (1998) 1011–1040.","apa":"Hausel, T. (1998). Vanishing of intersection numbers on the moduli space of Higgs bundles. <i>Advances in Theoretical and Mathematical Physics</i>. International Press. <a href=\"https://doi.org/10.4310/ATMP.1998.v2.n5.a3\">https://doi.org/10.4310/ATMP.1998.v2.n5.a3</a>","chicago":"Hausel, Tamás. “Vanishing of Intersection Numbers on the Moduli Space of Higgs Bundles.” <i>Advances in Theoretical and Mathematical Physics</i>. International Press, 1998. <a href=\"https://doi.org/10.4310/ATMP.1998.v2.n5.a3\">https://doi.org/10.4310/ATMP.1998.v2.n5.a3</a>."},"year":"1998","abstract":[{"lang":"eng","text":"In this paper we consider the topological side of a problem which is the analogue of Sen's S-duality testing conjecture for Hitchin's moduli space M of rank 2 stable Higgs bundles of fixed determinant of odd degree over a Riemann surface ∑. We prove that all intersection numbers in the compactly supported cohomology of M vanish, i.e. &quot;there are no topological L2 harmonic forms on M&quot;. This result generalizes the well known vanishing of the Euler characteristic of the moduli space of rank 2 stable bundles N of fixed determinant of odd degree over ∑. Our proof shows that the vanishing of all intersection numbers of H* cpt(M) is given by relations analogous to the Mumford relations in the cohomology ring of N."}],"date_created":"2018-12-11T11:52:06Z","_id":"1450","scopus_import":"1","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/math/9805071"}],"doi":"10.4310/ATMP.1998.v2.n5.a3","publication_identifier":{"issn":["1095-0761"]},"acknowledgement":"First of all I would like to thank my supervisor Nigel Hitchin for suggesting Problem 1, and for his help and \r\n encouragement. I am grateful to Michael Thaddeus for his inspiring paper [Thai], enlightening communications and his constant interest in my work. I am also indebted to Manfred Lehn for the idea of the proof of Theorem 6.2. I have found\r\nconversations with Michael Atiyah, Frances Kirwan and Graeme Segal very stimulating. I thank the Mathematical Institute and St. Catherine's College, Oxford for their hospitality during the preparation of this work. Finally I thank Trinity College, Cambridge for financial support.","article_type":"original","title":"Vanishing of intersection numbers on the moduli space of Higgs bundles","publication_status":"published","article_processing_charge":"No","oa_version":"Preprint"}]