A Lieb-Thirring bound for a magnetic Pauli Hamiltonian, II
Luca Bugliaro
ETH Hönggerberg, Zürich, SwitzerlandCharles Fefferman
Princeton University, United StatesGian Michele Graf
ETH Hönggerberg, Zürich, Switzerland
![A Lieb-Thirring bound for a magnetic Pauli Hamiltonian, II cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-rmi-volume-15-issue-3.png&w=3840&q=90)
Abstract
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.
Cite this article
Luca Bugliaro, Charles Fefferman, Gian Michele Graf, A Lieb-Thirring bound for a magnetic Pauli Hamiltonian, II. Rev. Mat. Iberoam. 15 (1999), no. 3, pp. 593–619
DOI 10.4171/RMI/266