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).
Abstract semiclassical analysis of the van Hove model
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In this paper we study the semiclassical limit $\hslash\to 0$ of a completely solvable model in quantum field theory: the van Hove model, describing a scalar field created and annihilated by an immovable source. Despite its simplicity, the van Hove model possesses many characterizing features of quantum fields, especially in the infrared region. In particular, the existence of non-Fock ground and equilibrium states in the presence of infrared singular sources makes a representation-independent algebraic approach of utmost importance. We make use of recent representation-independent techniques of infinite dimensional semiclassical analysis to establish the Bohr correspondence principle for the dynamics, equilibrium states, and long-time asymptotics in the van Hove model.
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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).