{"title":"Feynman-Kac formula for fiber Hamiltonians in the relativistic Nelson  model in two spatial dimensions","type":"preprint","project":[{"_id":"266","name":"PhoQC: PhoQC: Photonisches Quantencomputing"}],"date_updated":"2023-10-02T06:22:55Z","external_id":{"arxiv":["2309.09005"]},"_id":"47534","publication":"arXiv:2309.09005","year":"2023","language":[{"iso":"eng"}],"abstract":[{"text":"In this proceeding we consider a translation invariant Nelson type model in\r\ntwo spatial dimensions modeling a scalar relativistic particle in interaction\r\nwith a massive radiation field. As is well-known, the corresponding Hamiltonian\r\ncan be defined with the help of an energy renormalization. First, we review a\r\nFeynman-Kac formula for the semigroup generated by this Hamiltonian proven by\r\nthe authors in a recent preprint (where several matter particles and exterior\r\npotentials are treated as well). After that, we employ a few technical key\r\nrelations and estimates obtained in our preprint to present an otherwise\r\nself-contained derivation of new Feynman-Kac formulas for the fiber\r\nHamiltonians attached to fixed total momenta of the translation invariant\r\nsystem. We conclude by inferring an alternative derivation of the Feynman-Kac\r\nformula for the full translation invariant Hamiltonian.","lang":"eng"}],"user_id":"99427","citation":{"bibtex":"@article{Hinrichs_Matte_2023, title={Feynman-Kac formula for fiber Hamiltonians in the relativistic Nelson  model in two spatial dimensions}, journal={arXiv:2309.09005}, author={Hinrichs, Benjamin and Matte, Oliver}, year={2023} }","short":"B. Hinrichs, O. Matte, ArXiv:2309.09005 (2023).","chicago":"Hinrichs, Benjamin, and Oliver Matte. “Feynman-Kac Formula for Fiber Hamiltonians in the Relativistic Nelson  Model in Two Spatial Dimensions.” <i>ArXiv:2309.09005</i>, 2023.","apa":"Hinrichs, B., &#38; Matte, O. (2023). Feynman-Kac formula for fiber Hamiltonians in the relativistic Nelson  model in two spatial dimensions. In <i>arXiv:2309.09005</i>.","mla":"Hinrichs, Benjamin, and Oliver Matte. “Feynman-Kac Formula for Fiber Hamiltonians in the Relativistic Nelson  Model in Two Spatial Dimensions.” <i>ArXiv:2309.09005</i>, 2023.","ieee":"B. Hinrichs and O. Matte, “Feynman-Kac formula for fiber Hamiltonians in the relativistic Nelson  model in two spatial dimensions,” <i>arXiv:2309.09005</i>. 2023.","ama":"Hinrichs B, Matte O. Feynman-Kac formula for fiber Hamiltonians in the relativistic Nelson  model in two spatial dimensions. <i>arXiv:230909005</i>. Published online 2023."},"status":"public","date_created":"2023-10-02T06:21:37Z","department":[{"_id":"799"},{"_id":"623"}],"author":[{"full_name":"Hinrichs, Benjamin","id":"99427","orcid":"0000-0001-9074-1205","first_name":"Benjamin","last_name":"Hinrichs"},{"full_name":"Matte, Oliver","first_name":"Oliver","last_name":"Matte"}]}