### Abstract

We show that the Hamiltonian describing N nonrelativistic electrons with spin, interacting with the quantized radiation field and several fixed nuclei with total charge Z, has a ground state when N < Z+1. The result holds for any value of the fine structure constant α and for any value of the ultraviolet cutoff Λ on the radiation field. There is no infrared cutoff. The basic mathematical ingredient in our proof is a novel localization of the electromagnetic field in such a way that the errors in the energy are of smaller order than 1/L, where L is the localization radius.

Original language | English (US) |
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Pages (from-to) | 667-710 |

Number of pages | 44 |

Journal | Advances in Theoretical and Mathematical Physics |

Volume | 7 |

Issue number | 4 |

DOIs | |

State | Published - Jul 2003 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Physics and Astronomy(all)

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## Cite this

Lieb, E. H., & Loss, M. (2003). Existence of atoms and molecules in non-relativistic quantum electrodynamics.

*Advances in Theoretical and Mathematical Physics*,*7*(4), 667-710. https://doi.org/10.4310/ATMP.2003.v7.n4.a3