Jacob Schach Moeller
The translation invariant massive Nelson model: I. The bottom of the spectrum
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ABSTRACT.  In this paper we analyze the bottom of the energy-momentum spectrum of the translation invariant Nelson model, describing one electron linearly coupled to a second quantized massive scalar field. Our results are non-perturbative and include an HVZ theorem, 
non-degeneracy of ground states, existence of isolated groundstates in dimensions $1$ and $2$, non-existence of ground states embedded in the bottom of the essential spectrum in dimensions $3$ and $4$, (i.e., at total momenta where no isolated groundstate eigenvalue exists), and we study regularity and monotonicity properties of the bottom of the essential spectrum, as a function of total momentum.