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Analyticity of the Ground State Energy for Massless Nelson Models

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Abstract

We show that the ground state energy of the translationally invariant Nelson model, describing a particle coupled to a relativistic field of massless bosons, is an analytic function of the coupling constant and the total momentum. We derive an explicit expression for the ground state energy which is used to determine the effective mass.

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Authors and Affiliations

  1. Department of Mathematics, University of Virginia, P. O. Box 400137, Charlottesville, VA, 22904-4137, USA

    Abdelmalek Abdesselam

  2. Department of Mathematics, Ludwig Maximilans University, Theresienstrasse 39, Munich, 80333, Germany

    David Hasler

Authors
  1. Abdelmalek Abdesselam
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  2. David Hasler
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Correspondence to Abdelmalek Abdesselam.

Additional information

Communicated by I. M. Sigal

On leave from: Department of Mathematics, College of William and Mary, Williamsburg VA, 23187-8795, USA.

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Abdesselam, A., Hasler, D. Analyticity of the Ground State Energy for Massless Nelson Models. Commun. Math. Phys. 310, 511–536 (2012). https://doi.org/10.1007/s00220-011-1407-6

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