Non-relativistic Pauli--Fierz Hamiltonian for less than two photons

TL;DR

This paper analyzes a Pauli--Fierz model with fewer than two photons, explicitly computing the resolvent to determine the spectrum of the Hamiltonian, independent of coupling and infrared cutoff.

Contribution

It provides an explicit resolvent calculation for the Pauli--Fierz Hamiltonian with less than two photons, revealing the spectrum without dependence on coupling or infrared cutoff.

Findings

Spectrum of the Hamiltonian is explicitly determined.

Results are independent of coupling constant $e$.

Findings hold regardless of infrared cutoff parameter R.

Abstract

We consider the Pauli--Fierz model, which describes a particle (an electron) coupled to the quantized electromagnetic field and limit the number of photons to less than 2. By computing \red{the resolvent explicitly}, we located the spectrum of the Hamiltonian mass. Our results do not depend on the coupling constant $e$ nor on the infrared cutoff parameter $R$.