For any distributional source, the van Hove-Miyatake model is renormalizable and both renormalization schemes yield the same dressed Hamiltonian: the free field second quantization dΓ(ϖ).
Asymptotics in Spin-Boson type models
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abstract
In this paper we investigate a family of models for a qubit interacting with a bosonic field. More precisely, we find asymptotic limits of the Hamiltonian as the strength of the interaction tends to infinity. The main result has two applications. First of all, we show that self-energy renormalisation schemes similar to that of the Nelson model will never give a physically interesting result. This is because any limit obtained through such a scheme would be independent of the qubit. Secondly, we find that exited states exist in the massive Spin-Boson models for sufficiently large interaction strengths. We are also able to compute the asymptotic limit of many physical quantities.
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Ultraviolet Renormalization of the van Hove-Miyatake Model: an Algebraic and Hamiltonian Approach
For any distributional source, the van Hove-Miyatake model is renormalizable and both renormalization schemes yield the same dressed Hamiltonian: the free field second quantization dΓ(ϖ).