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On Nelson-type Hamiltonians and abstract boundary conditions
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We construct Hamiltonians for systems of nonrelativistic particles linearly coupled to massive scalar bosons using abstract boundary conditions. The construction yields an explicit characterisation of the domain of self-adjointness in terms of boundary conditions that relate sectors with different numbers of bosons. We treat both models in which the Hamiltonian may be defined as a form perturbation of the free operator, such as Fr\"ohlich's polaron, and renormalisable models, such as the massive Nelson model.
Forward citations
Cited by 3 Pith papers
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Ultraviolet Renormalization of Spin Boson Models I. Normal and 2-Nilpotent Interactions
The paper proves that generalized spin-boson models with normal or 2-nilpotent interactions can be ultraviolet renormalized, with norm resolvent convergence of the regularized Hamiltonians to an explicitly constructed...
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On the Ergodicity of Renormalized Translation-Invariant Nelson-Type Semigroups
For negative coupling, the renormalized non-relativistic and semi-relativistic Nelson semigroups are positivity improving with respect to the Fröhlich cone at every total momentum, proven via Feynman-Kac functional in...
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Feynman-Kac formula for fiber Hamiltonians in the relativistic Nelson model in two spatial dimensions
Derives new Feynman-Kac formulas for fiber Hamiltonians of the 2D relativistic Nelson model by applying estimates from the authors' recent preprint.
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