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On the geometry of supersymmetric quantum mechanical systems
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0003-3456-5846
2008 (English)In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 49, no 6, 062101-1-062101-15 p.Article in journal (Refereed) Published
Abstract [en]

We consider some simple examples of supersymmetric quantum mechanical systems and explore their possible geometric interpretation with the help of geometric aspects of real Clifford algebras. This leads to natural extensions of the considered systems to higher dimensions and more complicated potentials.

Place, publisher, year, edition, pages
American Institute of Physics , 2008. Vol. 49, no 6, 062101-1-062101-15 p.
Keyword [en]
supersymmetric quantum mechanics, geometric algebra, Clifford algebra, supermembrane toy model, harmonic oscillator
National Category
Other Physics Topics Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-12835DOI: 10.1063/1.2937096ISI: 000257284400001Scopus ID: 2-s2.0-46449109389OAI: oai:DiVA.org:kth-12835DiVA: diva2:319228
Note
QC20100629Available from: 2010-05-16 Created: 2010-05-16 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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