Hyperfine Splitting in Non-relativistic QED: Uniqueness of the Dressed Hydrogen Atom Ground State

@article{Amour2011HyperfineSI,
  title={Hyperfine Splitting in Non-relativistic QED: Uniqueness of the Dressed Hydrogen Atom Ground State},
  author={Laurent Amour and J'er'emy Faupin},
  journal={Communications in Mathematical Physics},
  year={2011},
  volume={319},
  pages={425-450}
}
  • L. AmourJ. Faupin
  • Published 2 December 2011
  • Physics
  • Communications in Mathematical Physics
We consider a free hydrogen atom composed of a spin-$${\frac{1}{2}}$$ nucleus and a spin-$${\frac{1}{2}}$$ 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. 
View on Springer
arxiv.org
2 Citations

2 Citations

Degenerate perturbation theory for models of quantum field theory with symmetries

We consider Hamiltonians of models describing non-relativistic quantum mechanical matter coupled to a relativistic field of bosons. If the free Hamiltonian has an eigenvalue, we show that this…

Renormalization analysis for degenerate ground states

References

SHOWING 1-10 OF 27 REFERENCES

HYPERFINE SPLITTING OF THE DRESSED HYDROGEN ATOM GROUND STATE IN NON-RELATIVISTIC QED

We consider a spin-½ electron and a spin-½ nucleus interacting with the quantized electromagnetic field in the standard model of non-relativistic QED. For a fixed total momentum sufficiently small,…

Lowest energy states in nonrelativistic QED: atoms and ions in motion

Ground state degeneracy of the Pauli-Fierz Hamiltonian with spin

We consider an electron, spin 1/2, minimally coupled to the quantized radiation field in the nonrelativistic approximation, a situation defined by the Pauli-Fierz Hamiltonian $H$. There is no…

Renormalized Electron Mass in Nonrelativistic QED

Within the framework of nonrelativistic QED, we prove that, for small values of the coupling constant, the energy function, $${E_{\vec{P}}}$$, of a dressed electron is twice differentiable in the…

Infraparticle Scattering States in Non-Relativistic QED: I. The Bloch-Nordsieck Paradigm

We construct infraparticle scattering states for Compton scattering in the standard model of non-relativistic QED. In our construction, an infrared cutoff initially introduced to regularize the model…

Ground states in non-relativistic quantum electrodynamics

Abstract.The excited states of a charged particle interacting with the quantized electromagnetic field and an external potential all decay, but such a particle should have a true ground state – one…

Infrared-Finite Algorithms in QED: The Groundstate of an Atom Interacting with the Quantized Radiation Field

In this paper, the groundstate of a nonrelativistic atom, minimally coupled to the quantized radiation field, and its groundstate energy are constructed by an iteration scheme inspired by [10]. This…

The dressed mobile atoms and ions

QUANTUM ELECTRODYNAMICS OF CONFINED NONRELATIVISTIC PARTICLES

Abstract We consider a system of finitely many nonrelativistic, quantum mechanical electrons bound to static nuclei. The electrons are minimally coupled to the quantized electromagnetic field; but we…

Spectral Analysis for Systems of Atoms and Molecules Coupled to the Quantized Radiation Field

Abstract:We consider systems of static nuclei and electrons – atoms and molecules – coupled to the quantized radiation field. The interactions between electrons and the soft modes of the quantized…