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Some spectral bounds for Schrödinger operators with Hardy-type potentials
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0003-3456-5846
(English)Manuscript (preprint) (Other academic)
Keyword [en]
Schrödinger operator, Hardy inequality, ground state representation, transformation of quadratic form, bounds for negative spectrum
National Category
Mathematical Analysis Other Physics Topics
URN: urn:nbn:se:kth:diva-12843OAI: diva2:319249
QC20100629Available from: 2010-05-17 Created: 2010-05-17 Last updated: 2010-06-29Bibliographically approved
In thesis
1. Zero-energy states in supersymmetric matrix models
Open this publication in new window or tab >>Zero-energy states in supersymmetric matrix models
2010 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The work of this Ph.D. thesis in mathematics concerns the problem of determining existence, uniqueness, and structure of zero-energy states in supersymmetric matrix models, which arise from a quantum mechanical description of the physics of relativistic membranes, reduced Yang-Mills gauge theory, and of nonperturbative features of string theory, respectively M-theory. Several new approaches to this problem are introduced and considered in the course of seven scientific papers, including: construction by recursive methods (Papers A and D), deformations and alternative models (Papers B and C), averaging with respect to symmetries (Paper E), and weighted supersymmetry and index theory (Papers F and G). The mathematical tools used and developed for these approaches include Clifford algebras and associated representation theory, structure of supersymmetric quantum mechanics, as well as spectral theory of (matrix-) Schrödinger operators.

Place, publisher, year, edition, pages
Stockholm: KTH, 2010. 88 p.
Trita-MAT. MA, ISSN 1401-2278 ; 10:06
supermembrane matrix models, supersymmetric quantum mechanics, zero-energy states, Clifford algebra, matrix-valued Schrödinger operator, spectral theory, bounds for negative eigenvalues
National Category
Mathematics Other Physics Topics
urn:nbn:se:kth:diva-12846 (URN)978-91-7415-662-1 (ISBN)
Public defence
2010-06-04, Sal F3, KTH, Lindstedtsvägen 26, Stockholm, 14:00 (English)
QC20100629Available from: 2010-05-19 Created: 2010-05-17 Last updated: 2010-06-29Bibliographically approved

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