Analyticity of the self-energy in total momentum of an atom coupled to the quantized radiation field

TL;DR

This paper proves that the self-energy of a neutral atom with a small electric dipole moment, coupled to the quantized electromagnetic field, is a real-analytic function of its momentum using spectral renormalization techniques.

Contribution

It establishes the analyticity of the atom's self-energy in momentum for small dipole moments and momenta, advancing understanding of atom-field interactions.

Findings

Self-energy is real-analytic in momentum for small parameters

Uses Feshbach-Schur spectral renormalization group method

Provides rigorous mathematical proof of analyticity

Abstract

We study a neutral atom with a non-vanishing electric dipole moment coupled to the quantized electromagnetic field. For a sufficiently small dipole moment and small momentum, the one-particle (self-) energy of an atom is proven to be a real-analytic function of its momentum. The main ingredient of our proof is a suitable form of the Feshbach-Schur spectral renormalization group.