The renormalized Nelson model in the weak coupling limit

TL;DR

This paper analyzes the renormalized Nelson model with massless bosons in the weak coupling limit, showing that an effective Coulomb potential emerges from virtual quantum field excitations.

Contribution

It demonstrates how the Coulomb potential naturally arises as an effective interaction in the weak coupling limit of the renormalized Nelson model.

Findings

Coulomb potential emerges as an effective interaction

Virtual excitations mediate the particle interaction

Weak coupling limit leads to a simplified effective model

Abstract

The Nelson model describes non-relativistic particles coupled to a relativistic Bose scalar field. In this article, we study the renormalized version of the Nelson model with massless bosons in Davies' weak coupling limit. Our main result states that the two-body Coulomb potential emerges as an effective pair interaction between the particles, which arises from the exchange of virtual excitations of the quantum field.