Spectral Methods For Operators Of Mathematical Physics
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Spectral Methods for Operators of Mathematical Physics
This book presents recent results in the following areas: spectral analysis of one-dimensional Schrödinger and Jacobi operators, discrete WKB analysis of solutions of second order difference equations, and applications of functional models of non-selfadjoint operators. Several developments treated appear for the first time in a book. It is addressed to a wide group of specialists working in operator theory or mathematical physics.
Operators, Geometry and Quanta
Author: Dmitri Fursaev
language: en
Publisher: Springer Science & Business Media
Release Date: 2011-06-25
This book gives a detailed and self-contained introduction into the theory of spectral functions, with an emphasis on their applications to quantum field theory. All methods are illustrated with applications to specific physical problems from the forefront of current research, such as finite-temperature field theory, D-branes, quantum solitons and noncommutativity. In the first part of the book, necessary background information on differential geometry and quantization, including less standard material, is collected. The second part of the book contains a detailed description of main spectral functions and methods of their calculation. In the third part, the theory is applied to several examples (D-branes, quantum solitons, anomalies, noncommutativity). This book addresses advanced graduate students and researchers in mathematical physics with basic knowledge of quantum field theory and differential geometry. The aim is to prepare readers to use spectral functions in their own research, in particular in relation to heat kernels and zeta functions.