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Stability of relativistic matter with magnetic fields for nuclear charges up to the critical value
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
Departments of Mathematics and Physics, Princeton University.
Department of Physics, Princeton University.
2007 (English)In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 275, no 2, 479-489 p.Article in journal (Refereed) Published
Abstract [en]

We give a proof of stability of relativistic matter with magnetic fields all the way up to the critical value of the nuclear charge Z alpha = 2/pi.

Place, publisher, year, edition, pages
2007. Vol. 275, no 2, 479-489 p.
Keyword [en]
INSTABILITY; OPERATORS
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-7029DOI: 10.1007/s00220-007-0307-2ISI: 000248911300006Scopus ID: 2-s2.0-34548238250OAI: oai:DiVA.org:kth-7029DiVA: diva2:11906
Note
QC 20100708. Uppdaterad från Accepted till Published 20100708.Available from: 2007-04-25 Created: 2007-04-25 Last updated: 2017-12-14Bibliographically approved
In thesis
1. Hardy-Lieb-Thirring inequalities for eigenvalues of Schrödinger operators
Open this publication in new window or tab >>Hardy-Lieb-Thirring inequalities for eigenvalues of Schrödinger operators
2007 (English)Doctoral thesis, comprehensive summary (Other scientific)
Abstract [en]

This thesis is devoted to quantitative questions about the discrete spectrum of Schrödinger-type operators.

In Paper I we show that the Lieb-Thirring inequalities on moments of negative eigen¬values remain true, with possibly different constants, when the critical Hardy weight is subtracted from the Laplace operator.

In Paper II we prove that the one-dimensional analog of this inequality holds even for the critical value of the moment parameter. In Paper III we establish Hardy-Lieb-Thirring inequalities for fractional powers of the Laplace operator and, in particular, relativistic Schrödinger operators. We do so by first establishing Hardy-Sobolev inequalities for such operators. We also allow for the inclu¬sion of magnetic fields.

As an application, in Paper IV we give a proof of stability of relativistic matter with magnetic fields up to the critical value of the nuclear charge.

In Paper V we derive inequalities for moments of the real part and the modulus of the eigen¬values of Schrödinger operators with complex-valued potentials.

Place, publisher, year, edition, pages
Stockholm: KTH, 2007. vii, 28 p.
Series
Trita-MAT. MA, ISSN 1401-2278 ; 07:03
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-4344 (URN)978-91-7178-626-5 (ISBN)
Public defence
2007-05-09, Sal F3, KTH, Lindstedtsvägen 26, Stockholm, 09:00
Opponent
Supervisors
Note
QC 20100708Available from: 2007-04-25 Created: 2007-04-25 Last updated: 2010-07-08Bibliographically approved

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