Estimating the number of negative eigenvalues of a relativistic Hamiltonian with regular magnetic field

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dc.creatorIftimie, Viorel
dc.creatorMantoiu, Marius
dc.creatorPurice, Radu
dc.date2007-11-08
dc.date.accessioned2026-07-07T08:41:34Z
dc.date.available2026-07-07T08:41:34Z
dc.descriptionWe prove the analog of the Cwickel-Lieb-Rosenblum estimation for the number of negative eigenvalues of a relativistic Hamiltonian with magnetic field $B\in C^\infty_{\rm{pol}}(\mathbb R^d)$ and an electric potential $V\in L^1_{\rm{loc}}(\mathbb R^d)$, $V_-\in L^d(\mathbb R^d)\cap L^{d/2}(\mathbb R^d)$. Compared to the nonrelativistic case, this estimation involves both norms of $V_-$ in $L^{d/2}(\mathbb R^d)$ and in $L^{d}(\mathbb R^d)$. A direct consequence is a Lieb-Thirring inequality for the sum of powers of the absolute values of the negative eigenvalues.
dc.identifierhttps://arxiv.org/abs/0711.1233
dc.identifierhttp://arxiv.org/abs/0711.1233
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/141710
dc.subjectMathematical Physics
dc.subject81Q10, 47N50, 83A05
dc.titleEstimating the number of negative eigenvalues of a relativistic Hamiltonian with regular magnetic field
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