preprint
Feynman-Kac formula for fiber Hamiltonians in the relativistic Nelson model in two spatial dimensions
Benjamin
Hinrichs
author 994270000-0001-9074-1205
Oliver
Matte
author
799
department
623
department
PhoQC: PhoQC: Photonisches Quantencomputing
project
In this proceeding we consider a translation invariant Nelson type model in
two spatial dimensions modeling a scalar relativistic particle in interaction
with a massive radiation field. As is well-known, the corresponding Hamiltonian
can be defined with the help of an energy renormalization. First, we review a
Feynman-Kac formula for the semigroup generated by this Hamiltonian proven by
the authors in a recent preprint (where several matter particles and exterior
potentials are treated as well). After that, we employ a few technical key
relations and estimates obtained in our preprint to present an otherwise
self-contained derivation of new Feynman-Kac formulas for the fiber
Hamiltonians attached to fixed total momenta of the translation invariant
system. We conclude by inferring an alternative derivation of the Feynman-Kac
formula for the full translation invariant Hamiltonian.
2023
eng
arXiv:2309.09005
2309.09005
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.
Hinrichs, B., & Matte, O. (2023). Feynman-Kac formula for fiber Hamiltonians in the relativistic Nelson model in two spatial dimensions. In <i>arXiv:2309.09005</i>.
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.
@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} }
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.
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.
B. Hinrichs, O. Matte, ArXiv:2309.09005 (2023).
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