{"publication":"Journal of Mathematical Physics","year":"2022","date_updated":"2023-08-03T14:12:01Z","project":[{"call_identifier":"H2020","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png"},"article_type":"original","publication_identifier":{"issn":["0022-2488"]},"type":"journal_article","ec_funded":1,"abstract":[{"lang":"eng","text":"A recently proposed approach for avoiding the ultraviolet divergence of Hamiltonians with particle creation is based on interior-boundary conditions (IBCs). The approach works well in the non-relativistic case, i.e., for the Laplacian operator. Here, we study how the approach can be applied to Dirac operators. While this has successfully been done already in one space dimension, and more generally for codimension-1 boundaries, the situation of point sources in three dimensions corresponds to a codimension-3 boundary. One would expect that, for such a boundary, Dirac operators do not allow for boundary conditions because they are known not to allow for point interactions in 3D, which also correspond to a boundary condition. Indeed, we confirm this expectation here by proving that there is no self-adjoint operator on a (truncated) Fock space that would correspond to a Dirac operator with an IBC at configurations with a particle at the origin. However, we also present a positive result showing that there are self-adjoint operators with an IBC (on the boundary consisting of configurations with a particle at the origin) that are away from those configurations, given by a Dirac operator plus a sufficiently strong Coulomb potential."}],"date_created":"2023-01-08T23:00:53Z","file":[{"date_created":"2023-01-20T11:58:59Z","checksum":"5150287295e0ce4f12462c990744d65d","creator":"dernst","success":1,"content_type":"application/pdf","file_id":"12327","date_updated":"2023-01-20T11:58:59Z","relation":"main_file","access_level":"open_access","file_name":"2022_JourMathPhysics_Henheik.pdf","file_size":5436804}],"citation":{"mla":"Henheik, Sven Joscha, and Roderich Tumulka. “Interior-Boundary Conditions for the Dirac Equation at Point Sources in Three Dimensions.” <i>Journal of Mathematical Physics</i>, vol. 63, no. 12, 122302, AIP Publishing, 2022, doi:<a href=\"https://doi.org/10.1063/5.0104675\">10.1063/5.0104675</a>.","ista":"Henheik SJ, Tumulka R. 2022. Interior-boundary conditions for the Dirac equation at point sources in three dimensions. Journal of Mathematical Physics. 63(12), 122302.","short":"S.J. Henheik, R. Tumulka, Journal of Mathematical Physics 63 (2022).","ama":"Henheik SJ, Tumulka R. Interior-boundary conditions for the Dirac equation at point sources in three dimensions. <i>Journal of Mathematical Physics</i>. 2022;63(12). doi:<a href=\"https://doi.org/10.1063/5.0104675\">10.1063/5.0104675</a>","chicago":"Henheik, Sven Joscha, and Roderich Tumulka. “Interior-Boundary Conditions for the Dirac Equation at Point Sources in Three Dimensions.” <i>Journal of Mathematical Physics</i>. AIP Publishing, 2022. <a href=\"https://doi.org/10.1063/5.0104675\">https://doi.org/10.1063/5.0104675</a>.","apa":"Henheik, S. J., &#38; Tumulka, R. (2022). Interior-boundary conditions for the Dirac equation at point sources in three dimensions. <i>Journal of Mathematical Physics</i>. AIP Publishing. <a href=\"https://doi.org/10.1063/5.0104675\">https://doi.org/10.1063/5.0104675</a>","ieee":"S. J. Henheik and R. Tumulka, “Interior-boundary conditions for the Dirac equation at point sources in three dimensions,” <i>Journal of Mathematical Physics</i>, vol. 63, no. 12. AIP Publishing, 2022."},"article_processing_charge":"No","intvolume":"        63","month":"12","language":[{"iso":"eng"}],"acknowledgement":"J.H. gratefully acknowledges the partial financial support by the ERC Advanced Grant “RMTBeyond” under Grant No. 101020331.\r\n","ddc":["510"],"has_accepted_license":"1","status":"public","day":"01","date_published":"2022-12-01T00:00:00Z","scopus_import":"1","volume":63,"file_date_updated":"2023-01-20T11:58:59Z","department":[{"_id":"LaEr"}],"quality_controlled":"1","_id":"12110","doi":"10.1063/5.0104675","oa_version":"Published Version","author":[{"first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","orcid":"0000-0003-1106-327X","full_name":"Henheik, Sven Joscha","last_name":"Henheik"},{"full_name":"Tumulka, Roderich","last_name":"Tumulka","first_name":"Roderich"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication_status":"published","external_id":{"isi":["000900748900002"]},"license":"https://creativecommons.org/licenses/by/4.0/","publisher":"AIP Publishing","issue":"12","article_number":"122302","oa":1,"isi":1,"title":"Interior-boundary conditions for the Dirac equation at point sources in three dimensions"}