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- W4386875229 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." @default.
- W4386875229 created "2023-09-20" @default.
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- W4386875229 date "2023-09-16" @default.
- W4386875229 modified "2023-09-27" @default.
- W4386875229 title "Feynman-Kac formula for fiber Hamiltonians in the relativistic Nelson model in two spatial dimensions" @default.
- W4386875229 doi "https://doi.org/10.48550/arxiv.2309.09005" @default.
- W4386875229 hasPublicationYear "2023" @default.
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