@unpublished{47534,
abstract = {{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.}},
author = {{Hinrichs, Benjamin and Matte, Oliver}},
booktitle = {{arXiv:2309.09005}},
title = {{{Feynman-Kac formula for fiber Hamiltonians in the relativistic Nelson model in two spatial dimensions}}},
year = {{2023}},
}