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July 2003 Existence of Atoms and Molecules in Non-Relativistic Quantum Electrodynamics
Elliott H. Lieb, Michael Loss
Adv. Theor. Math. Phys. 7(4): 667-710 (July 2003).


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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Elliott H. Lieb. Michael Loss. "Existence of Atoms and Molecules in Non-Relativistic Quantum Electrodynamics." Adv. Theor. Math. Phys. 7 (4) 667 - 710, July 2003.


Published: July 2003
First available in Project Euclid: 4 April 2005

zbMATH: 1058.81080
MathSciNet: MR2039034

Rights: Copyright © 2003 International Press of Boston

Vol.7 • No. 4 • July 2003
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