Hyperfine splitting in non-relativistic QED: uniqueness of the dressed hydrogen atom ground state

TL;DR

This paper proves the uniqueness of the ground state in a non-relativistic QED model of hydrogen, capturing the hyperfine structure, for small fine-structure constants.

Contribution

It establishes the uniqueness of the hydrogen atom's ground state within a non-relativistic QED framework, highlighting hyperfine effects.

Findings

Ground state is unique for small fine-structure constants

Results reflect the hyperfine structure of hydrogen

Supports the stability analysis of the hydrogen atom in QED

Abstract

We consider a free hydrogen atom composed of a spin-1/2 nucleus and a spin-1/2 electron in the standard model of non-relativistic QED. We study the Pauli-Fierz Hamiltonian associated with this system at a fixed total momentum. For small enough values of the fine-structure constant, we prove that the ground state is unique. This result reflects the hyperfine structure of the hydrogen atom ground state.