On dilation analyticity and spatial exponential decay of atomic ground states in non-relativistic qed

TL;DR

This paper proves that the ground state and energy of a spinless electron atom in non-relativistic quantum electrodynamics depend analytically on dilation, phase, and coupling parameters, leading to exponential spatial decay without infrared regularization.

Contribution

It establishes dilation analyticity and exponential decay of atomic ground states in non-relativistic QED without infrared regularization, using operator theoretic renormalization.

Findings

Ground state energy and state depend analytically on dilation and phase parameters.

Ground state exhibits exponential spatial decay.

No infrared regularization needed for decay results.

Abstract

We consider the ground state and the ground state energy of an atom with spinless electrons in the framework of non-relativistic qed. We show that the ground state energy as well as the ground state depend analytically on the parameters of the group of dilations, the parameter of a group of spatial dependent phase changes, and on the minimal coupling constant. As a corollary we obtain spatial exponential decay of the ground state as well as of its dilation analytic extension. No infrared regularization is needed for the result. Our result is based on operator theoretic renormalization.