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arXiv · 1803.00872

On Nelson-type Hamiltonians and abstract boundary conditions

Jonas Lampart·Julian Schmidt
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Abstract

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.

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Jonas Lampart, Julian Schmidt. 2018-03-02. On Nelson-type Hamiltonians and abstract boundary conditions. https://doi.org/10.1007/s00220-019-03294-x

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