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 valid for all values of the coupling constant 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.
Communicated by Joel Feldman
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submitted 04/11/04, accepted 17/02/05
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Møller, J.S. The Translation Invariant Massive Nelson Model: I. The Bottom of the Spectrum. Ann. Henri Poincaré 6, 1091–1135 (2005). https://doi.org/10.1007/s00023-005-0234-8
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DOI: https://doi.org/10.1007/s00023-005-0234-8