The dressed mobile atoms and ions

TL;DR

This paper analyzes the spectral properties of free atoms and ions interacting with quantized electromagnetic fields, establishing conditions for ground states and characterizing the spectrum, with implications for quantum electrodynamics.

Contribution

It proves the existence of ground states for atoms and ions under certain conditions and determines the spectrum of the reduced Hamiltonian in a magnetic field.

Findings

Ground state existence for atoms with small coupling and momentum

Additional infrared regularization needed for ions

Determination of the absolutely continuous spectrum

Abstract

We consider free atoms and ions in $\R^3$ interacting with the quantized electromagnetic field. Because of the translation invariance we consider the reduced hamiltonian associated with the total momentum. After introducing an ultraviolet cutoff we prove that the reduced hamiltonian for atoms has a ground state if the coupling constant and the total momentum are sufficiently small. In the case of ions an extra infrared regularization is needed. We also consider the case of the hydrogen atom in a constant magnetic field. Finally we determine the absolutely continuous spectrum of the reduced hamiltonian.