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Zero-energy states in supersymmetric matrix models

by Lundholm, Douglas, PhD

Abstract (Summary)
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.
Bibliographical Information:

Advisor:

School:Kungliga Tekniska högskolan

School Location:Sweden

Source Type:Doctoral Dissertation

Keywords:MATHEMATICS; Algebra, geometry and mathematical analysis; NATURAL SCIENCES; Physics; Other physics; Mathematical physics; supermembrane matrix models; supersymmetric quantum mechanics; zero-energy states; Clifford algebra; matrix-valued Schrödinger operator; spectral theory; bounds for negative eigenvalues

ISBN:978-91-7415-662-1

Date of Publication:01/01/2010

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