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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Luca Bugliaro, Gian Michele Graf, Charles Fefferman, A Lieb-Thirring bound for a magnetic Pauli Hamiltonian, II. Rev. Mat. Iberoam. 15 (1999), no. 3, pp. 593–619DOI 10.4171/RMI/266