Advances in Theoretical and Mathematical Physics

Volume 7 (2003)

Number 4

Existence of Atoms and Molecules in Non-Relativistic Quantum Electrodynamics

Pages: 667 – 710



Elliott H. Lieb

Michael Loss


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 $N$ is less than $Z+1$. The result holds for any value of the fine structure constant $\alpha$ and for any value of the ultraviolet cutoff $\Lambda$ 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.

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