The Magnetic Scott Correction for Relativistic Matter at Criticality

Abstract

We provide a proof of the first correction to the leading asymptotics of the minimal energy of pseudo-relativistic molecules in the presence of magnetic fields, the so-called "relativistic Scott correction", when $\max Z_k\alpha \le 2/\pi$, where $Z_k$ is the charge of the $k$-th nucleus and $\alpha$ is the fine structure constant. Our theorem extends a previous result by Erdős, Fournais, and Solovej to the critical constant $2/\pi$ in the relativistic Hardy inequality $|p|-\frac{2}{\pi |x|}\ge 0$.

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• Hardy-Lieb-Thirring Inequalities for Fractional Pauli Operators