References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt152",{id:"formSmash:upper:j_idt152",widgetVar:"widget_formSmash_upper_j_idt152",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt153_j_idt156",{id:"formSmash:upper:j_idt153:j_idt156",widgetVar:"widget_formSmash_upper_j_idt153_j_idt156",target:"formSmash:upper:j_idt153:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

Zero-energy states in supersymmetric matrix modelsPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2010 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Stockholm: KTH , 2010. , 88 p.
##### Series

Trita-MAT. MA, ISSN 1401-2278 ; 10:06
##### Keyword [en]

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
##### Identifiers

URN: urn:nbn:se:kth:diva-12846ISBN: 978-91-7415-662-1OAI: oai:DiVA.org:kth-12846DiVA: diva2:319330
##### Public defence

2010-06-04, Sal F3, KTH, Lindstedtsvägen 26, Stockholm, 14:00 (English)
##### Opponent

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt455",{id:"formSmash:j_idt455",widgetVar:"widget_formSmash_j_idt455",multiple:true});
##### Supervisors

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt461",{id:"formSmash:j_idt461",widgetVar:"widget_formSmash_j_idt461",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt467",{id:"formSmash:j_idt467",widgetVar:"widget_formSmash_j_idt467",multiple:true});
##### Note

QC20100629Available from: 2010-05-19 Created: 2010-05-17 Last updated: 2010-06-29Bibliographically approved
##### List of papers

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.

1. Dynamical Symmetries in Supersymmetric Matrix$(function(){PrimeFaces.cw("OverlayPanel","overlay319243",{id:"formSmash:j_idt503:0:j_idt507",widgetVar:"overlay319243",target:"formSmash:j_idt503:0:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

2. On the geometry of supersymmetric quantum mechanical systems$(function(){PrimeFaces.cw("OverlayPanel","overlay319228",{id:"formSmash:j_idt503:1:j_idt507",widgetVar:"overlay319228",target:"formSmash:j_idt503:1:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

3. Octonionic twists for supermembrane matrix models$(function(){PrimeFaces.cw("OverlayPanel","overlay319245",{id:"formSmash:j_idt503:2:j_idt507",widgetVar:"overlay319245",target:"formSmash:j_idt503:2:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

4. Construction of the zero-energy state of SU(2)-matrix theory: Near the origin$(function(){PrimeFaces.cw("OverlayPanel","overlay319246",{id:"formSmash:j_idt503:3:j_idt507",widgetVar:"overlay319246",target:"formSmash:j_idt503:3:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

5. Spin(9) average of SU(N) matrix models$(function(){PrimeFaces.cw("OverlayPanel","overlay319247",{id:"formSmash:j_idt503:4:j_idt507",widgetVar:"overlay319247",target:"formSmash:j_idt503:4:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

6. Weighted Supermembrane Toy Model$(function(){PrimeFaces.cw("OverlayPanel","overlay319248",{id:"formSmash:j_idt503:5:j_idt507",widgetVar:"overlay319248",target:"formSmash:j_idt503:5:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

7. Some spectral bounds for Schrödinger operators with Hardy-type potentials$(function(){PrimeFaces.cw("OverlayPanel","overlay319249",{id:"formSmash:j_idt503:6:j_idt507",widgetVar:"overlay319249",target:"formSmash:j_idt503:6:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_lower_j_idt1196",{id:"formSmash:lower:j_idt1196",widgetVar:"widget_formSmash_lower_j_idt1196",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:lower:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt1197_j_idt1199",{id:"formSmash:lower:j_idt1197:j_idt1199",widgetVar:"widget_formSmash_lower_j_idt1197_j_idt1199",target:"formSmash:lower:j_idt1197:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});