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Existence and non existence of a ground state for the massless Nelson model under binding condition
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Existence and non existence of a ground state for the massless Nelson model under binding condition
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We consider a model describing $N$ non-relativistic particles coupled to a massless quantum scalar field, called \emph{Nelson model}, under a binding condition on the external potential. We prove that this model does not admit ground state in the Fock representation of the canonical commutation relations, but it does in another not unitarily equivalent coherent representation. Remark that the binding condition is satisfied for small values of the coupling constant.
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Cited by 1 Pith paper
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Spectral Analysis of a Soft Quantum Waveguide Coupled to a Massive Quantum Scalar Field
For a Nelson-type Hamiltonian on a soft quantum waveguide, the essential spectrum of the curved guide is a half-line whose threshold combines the straight-guide ionization threshold and the one-boson mass; a negative ...
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