Infrared regular representation of the three dimensional massless Nelson model

TL;DR

This paper establishes the absolute continuity of the t=0 projection of the interacting measure with a Gaussian measure in the Euclidean representation of the 3D massless Nelson model and identifies the corresponding Hamiltonian.

Contribution

It provides a detailed analysis of the Euclidean representation of the 3D massless Nelson model, including the regularity of the measure and the explicit form of the Hamiltonian.

Findings

t=0 projection is absolutely continuous w.r.t. Gaussian measure

Hamiltonian in Fock space is explicitly determined

Euclidean measure representation is characterized

Abstract

We prove that in the Euclidean representation of the three dimensional massless Nelson model the t = 0 projection of the interacting measure is absolutely continuous with respect to a Gaussian measure with suitably adjusted mean. We also determine the Hamiltonian in the Fock space over this Gaussian measure space.