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Weighted Supermembrane Toy Model
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0003-3456-5846
2010 (English)In: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 92, no 2, 125-141 p.Article in journal (Refereed) Published
Abstract [en]

A weighted Hilbert space approach to the study of zero-energy states of supersymmetric matrix models is introduced. Applied to a related but technically simpler model, it is shown that the spectrum of the corresponding weighted Hamiltonian simplifies to become purely discrete for sufficient weights. This follows from a bound for the number of negative eigenvalues of an associated matrix-valued Schrodinger operator.

Place, publisher, year, edition, pages
Springer Netherlands , 2010. Vol. 92, no 2, 125-141 p.
Keyword [en]
supersymmetric quantum mechanics, matrix models, zero-energy states, weighted Hilbert spaces, matrix-valued Schrödinger operator, Cwikel-Lieb-Rozenblum inequality
National Category
Other Physics Topics Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-12842DOI: 10.1007/s11005-010-0383-7ISI: 000277243800003Scopus ID: 2-s2.0-77952092107OAI: oai:DiVA.org:kth-12842DiVA: diva2:319248
Note
QC20100629Available from: 2010-05-17 Created: 2010-05-17 Last updated: 2017-12-12Bibliographically 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.
Series
Trita-MAT. MA, ISSN 1401-2278 ; 10:06
Keyword
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: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)
Opponent
Supervisors
Note
QC20100629Available from: 2010-05-19 Created: 2010-05-17 Last updated: 2010-06-29Bibliographically approved

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Lundholm, Douglas

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