{"type":"preprint","citation":{"ama":"Hinrichs B, Matte O. Feynman-Kac formula and asymptotic behavior of the minimal energy for  the relativistic Nelson model in two spatial dimensions.","bibtex":"@article{Hinrichs_Matte, title={Feynman-Kac formula and asymptotic behavior of the minimal energy for  the relativistic Nelson model in two spatial dimensions}, author={Hinrichs, Benjamin and Matte, Oliver} }","ieee":"B. Hinrichs and O. Matte, “Feynman-Kac formula and asymptotic behavior of the minimal energy for  the relativistic Nelson model in two spatial dimensions.” .","short":"B. Hinrichs, O. Matte, (n.d.).","apa":"Hinrichs, B., &#38; Matte, O. (n.d.). <i>Feynman-Kac formula and asymptotic behavior of the minimal energy for  the relativistic Nelson model in two spatial dimensions</i>.","mla":"Hinrichs, Benjamin, and Oliver Matte. <i>Feynman-Kac Formula and Asymptotic Behavior of the Minimal Energy for  the Relativistic Nelson Model in Two Spatial Dimensions</i>.","chicago":"Hinrichs, Benjamin, and Oliver Matte. “Feynman-Kac Formula and Asymptotic Behavior of the Minimal Energy for  the Relativistic Nelson Model in Two Spatial Dimensions,” n.d."},"date_created":"2023-04-14T05:03:59Z","publication_status":"submitted","external_id":{"arxiv":["2211.14046"]},"_id":"43498","status":"public","year":"2022","author":[{"first_name":"Benjamin","id":"99427","full_name":"Hinrichs, Benjamin","last_name":"Hinrichs","orcid":"0000-0001-9074-1205"},{"first_name":"Oliver","last_name":"Matte","full_name":"Matte, Oliver"}],"user_id":"99427","title":"Feynman-Kac formula and asymptotic behavior of the minimal energy for  the relativistic Nelson model in two spatial dimensions","abstract":[{"lang":"eng","text":"We consider the renormalized relativistic Nelson model in two spatial\r\ndimensions for a finite number of spinless, relativistic quantum mechanical\r\nmatter particles in interaction with a massive scalar quantized radiation\r\nfield. We find a Feynman-Kac formula for the corresponding semigroup and\r\ndiscuss some implications such as ergodicity and weighted $L^p$ to $L^q$\r\nbounds, for external potentials that are Kato decomposable in the suitable\r\nrelativistic sense. Furthermore, our analysis entails upper and lower bounds on\r\nthe minimal energy for all values of the involved physical parameters when the\r\nPauli principle for the matter particles is ignored. In the translation\r\ninvariant case (no external potential) these bounds permit to compute the\r\nleading asymptotics of the minimal energy in the three regimes where the number\r\nof matter particles goes to infinity, the coupling constant for the\r\nmatter-radiation interaction goes to infinity and the boson mass goes to zero."}],"extern":"1","language":[{"iso":"eng"}],"date_updated":"2023-04-14T05:06:21Z"}