Revista Matemática Iberoamericana

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Volume 15, Issue 3, 1999, pp. 593–619
DOI: 10.4171/RMI/266

Published online: 1999-12-31

A Lieb-Thirring bound for a magnetic Pauli Hamiltonian, II

Luca Bugliaro[1], Gian Michele Graf[2] and Charles Fefferman[3]

(1) ETH Hönggerberg, Zürich, Switzerland
(2) ETH Hönggerberg, Zürich, Switzerland
(3) Princeton University, United States

We establish a Lieb-Thirring type estimate for Pauli Hamiltonians with nonhomogeneous magnetic fields. Besides of depending on the size of the field the bound also takes into account the size of the field gradient. We then apply the inequality to prove stability of non-relativistic quantum mechanical matter coupled to the quantized ultraviolet-cutoff electromagnetic field for arbitrary values of the fine structure constant.

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Bugliaro Luca, Graf Gian Michele, Fefferman Charles: A Lieb-Thirring bound for a magnetic Pauli Hamiltonian, II. Rev. Mat. Iberoam. 15 (1999), 593-619. doi: 10.4171/RMI/266