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Analyticity of the Ground State Energy for Massless Nelson Models


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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Correspondence to Abdelmalek Abdesselam.

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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).

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  • Ground State Energy
  • Positivity Preserve
  • Harmonic Oscillator Potential
  • Nelson Model
  • Path Integral Representation