Zero-energy states in supersymmetric matrix models
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.
School:Kungliga Tekniska högskolan
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
Date of Publication:01/01/2010