Non-Fock Ground States in the Translation-Invariant Nelson Model Revisited Non-Perturbatively

TL;DR

This paper provides a non-perturbative proof for the existence of dressed one-particle states in the translation-invariant Nelson model, addressing the infrared problem and extending results to both non- and semi-relativistic cases.

Contribution

It introduces a simple non-perturbative method to establish the existence of dressed states at arbitrary coupling and most momenta in the Nelson model.

Findings

Existence of dressed one-particle states at arbitrary coupling.

Results valid for both non- and semi-relativistic Nelson models.

Applicable to almost all total momenta in a specific momentum region.

Abstract

The Nelson model, describing a quantum mechanical particle linearly coupled to a bosonic field, exhibits the infrared problem in the sense that no ground state exists at arbitrary total momentum. However, passing to a non-Fock representation, one can prove the existence of so-called dressed one-particle states. In this article, we give a simple non-perturbative proof for the existence of such one-particle states at arbitrary coupling strength and for almost all total momenta in a physically motivated momentum region. Our results hold both for the non- and the semi-relativistic Nelson model.