Analyticity of The Ground State Energy For Massless Nelson Models

Abdelmalek Abdesselam, David Hasler

Published 2010-08-27, updated 2011-08-03Version 2

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.