Absence of Ground States in the Renormalized Massless Translation-Invariant Nelson Model

Abstract

We consider a model for a massive uncharged non-relativistic particle interacting with a massless bosonic field, widely referred to as the Nelson model. It is well known, that an ultraviolet renormalized Hamilton operator exists in this case. Further, due to translation-invariance, it decomposes into fiber operators. In this paper, we treat the renormalized fiber operators. We give a description of the operator and form domains and prove that the fiber operators do not have a ground state. Our results hold for any non-zero coupling constant and arbitrary total momentum. Our proof for the absence of ground states is a new generalization of methods recently applied to related models. A major enhancement we provide, is that the method can be applied to models with degenerate ground state eigenspaces.

arXiv commentversion accepted for publication in Rev. Math. Phys

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Cited by in corpus (5)

• On Existence of Ground States in the Spin Boson Model
• Ground states and associated path measures in the renormalized Nelson model
• Non-Fock Ground States in the Translation-Invariant Nelson Model Revisited Non-Perturbatively
• A Lower Bound on the Critical Momentum of an Impurity in a Bose-Einstein Condensate
• On renormalized Hamiltonian nets