### 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 A 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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Title of host publication | The Stability of Matter |

Subtitle of host publication | From Atoms to Stars: Fourth Edition |

Publisher | Springer Berlin Heidelberg |

Pages | 665-708 |

Number of pages | 44 |

ISBN (Print) | 3540420835, 9783540222125 |

DOIs | |

State | Published - Jan 1 2005 |

### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

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## Cite this

Lieb, E. H., & Loss, M. (2005). Existence of atoms and molecules in non-relativistic quantum electrodynamics. In

*The Stability of Matter: From Atoms to Stars: Fourth Edition*(pp. 665-708). Springer Berlin Heidelberg. https://doi.org/10.1007/3-540-27056-6_42