Analyticity of The Ground State Energy For Massless Nelson Models

TL;DR

This paper proves that the ground state energy in the massless Nelson model is analytic with respect to coupling and momentum, providing explicit formulas to analyze effective mass.

Contribution

It establishes the analyticity of the ground state energy in the massless Nelson model and derives explicit expressions for it.

Findings

Ground state energy is analytic in coupling and momentum.

Explicit formula for the ground state energy.

Determination of the effective mass from the energy expression.

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.