A Window into Zeta and Modular Physics
by Klaus Kirsten, Floyd L. Williams
Publisher: Cambridge University Press 2010
Number of pages: 351
This book provides an introduction, with applications, to three interconnected mathematical topics: zeta functions in their rich variety; modular forms; vertex operator algebras. Applications of the material to physics are presented.
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by A. Pankov - Vinnitsa State Pedagogical University
Contents: Operators in Hilbert spaces; Spectral theorem of self-adjoint operators; Compact operators and the Hilbert-Schmidt theorem; Perturbation of discrete spectrum; Variational principles; One-dimensional Schroedinger operator; etc.
by Douglas Lundholm, Lars Svensson - arXiv
These are lecture notes for a course on the theory of Clifford algebras. The various applications include vector space and projective geometry, orthogonal maps and spinors, normed division algebras, as well as simplicial complexes and graph theory.
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We consider integrable Hamiltonian systems in a general setting of invariant submanifolds which need not be compact. This is the case a global Kepler system, non-autonomous integrable Hamiltonian systems and systems with time-dependent parameters.
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These are the lecture notes for a one semester course at Leibniz University Hannover. The main aim of the course is to give an introduction to the mathematical methods used in describing discrete quantum systems consisting of infinitely many sites.