Spectral Analysis of Relativistic Operators

Spectral Analysis of Relativistic Operators
Author: A. A. Balinsky
Publisher: World Scientific
Total Pages: 200
Release: 2011
Genre: Science
ISBN: 1848162189

Over the last decade, there has been considerable interest and progress in determining the spectral properties of various operators that take relativistic effects into account, with important implications for mathematics and physics. Difficulties are encountered in many-particle problems due to the lack of semiboundedness of the Dirac operator, and this has led to the investigation of operators like those of Chandrasekhar-Herbst and Brown-Ravenhall, which are semibounded under appropriate circumstances.This book contains an up-to-date, comprehensive and self-contained analysis of the spectral properties of these operators, providing the tools for anyone working in this area. Another major feature is the work of the authors on zero modes, a topic which has important significance for the stability of matter and other physical problems. Up until now, these topics have been scattered throughout the literature, without a systematic and cohesive treatment. The book will report largely on the progress on these topics published since 1992.

Spectral Analysis Of Relativistic Operators

Spectral Analysis Of Relativistic Operators
Author: William Desmond Evans
Publisher: World Scientific
Total Pages: 200
Release: 2010-10-15
Genre: Science
ISBN: 1908978821

Over the last decade, there has been considerable interest and progress in determining the spectral properties of various operators that take relativistic effects into account, with important implications for mathematics and physics. Difficulties are encountered in many-particle problems due to the lack of semiboundedness of the Dirac operator, and this has led to the investigation of operators like those of Chandrasekhar-Herbst and Brown-Ravenhall, which are semibounded under appropriate circumstances.This book contains an up-to-date, comprehensive and self-contained analysis of the spectral properties of these operators, providing the tools for anyone working in this area. Another major feature is the work of the authors on zero modes, a topic which has important significance for the stability of matter and other physical problems. Up until now, these topics have been scattered throughout the literature, without a systematic and cohesive treatment. The book will report largely on the progress on these topics published since 1992./a

Elliptic Differential Operators and Spectral Analysis

Elliptic Differential Operators and Spectral Analysis
Author: D. E. Edmunds
Publisher: Springer
Total Pages: 324
Release: 2018-11-20
Genre: Mathematics
ISBN: 3030021254

This book deals with elliptic differential equations, providing the analytic background necessary for the treatment of associated spectral questions, and covering important topics previously scattered throughout the literature. Starting with the basics of elliptic operators and their naturally associated function spaces, the authors then proceed to cover various related topics of current and continuing importance. Particular attention is given to the characterisation of self-adjoint extensions of symmetric operators acting in a Hilbert space and, for elliptic operators, the realisation of such extensions in terms of boundary conditions. A good deal of material not previously available in book form, such as the treatment of the Schauder estimates, is included. Requiring only basic knowledge of measure theory and functional analysis, the book is accessible to graduate students and will be of interest to all researchers in partial differential equations. The reader will value its self-contained, thorough and unified presentation of the modern theory of elliptic operators.

Spectral Theory and Differential Equations

Spectral Theory and Differential Equations
Author: E. Khruslov
Publisher: American Mathematical Society
Total Pages: 266
Release: 2014-09-26
Genre: Mathematics
ISBN: 1470416832

This volume is dedicated to V. A. Marchenko on the occasion of his 90th birthday. It contains refereed original papers and survey articles written by his colleagues and former students of international stature and focuses on the areas to which he made important contributions: spectral theory of differential and difference operators and related topics of mathematical physics, including inverse problems of spectral theory, homogenization theory, and the theory of integrable systems. The papers in the volume provide a comprehensive account of many of the most significant recent developments in that broad spectrum of areas.

Feynman-Kac-Type Formulae and Gibbs Measures

Feynman-Kac-Type Formulae and Gibbs Measures
Author: József Lörinczi
Publisher: Walter de Gruyter GmbH & Co KG
Total Pages: 576
Release: 2020-01-20
Genre: Mathematics
ISBN: 3110330393

This is the second updated and extended edition of the successful book on Feynman-Kac theory. It offers a state-of-the-art mathematical account of functional integration methods in the context of self-adjoint operators and semigroups using the concepts and tools of modern stochastic analysis. The first volume concentrates on Feynman-Kac-type formulae and Gibbs measures.

Unstable States in the Continuous Spectra. Analysis, Concepts, Methods and Results

Unstable States in the Continuous Spectra. Analysis, Concepts, Methods and Results
Author:
Publisher: Academic Press
Total Pages: 565
Release: 2010-11-25
Genre: Science
ISBN: 0123809010

Advances in Quantum Chemistry presents surveys of current developments in this rapidly developing field. With invited reviews written by leading international researchers, each presenting new results, it provides a single vehicle for following progress in this interdisciplinary area. - Publishes articles, invited reviews and proceedings of major international conferences and workshops - Written by leading international researchers in quantum and theoretical chemistry - Highlights important interdisciplinary developments

Complex Quantum Systems: Analysis Of Large Coulomb Systems

Complex Quantum Systems: Analysis Of Large Coulomb Systems
Author: Heinz Siedentop
Publisher: World Scientific
Total Pages: 303
Release: 2013-05-20
Genre: Science
ISBN: 9814460168

This volume is based on lectures given during the program “Complex Quantum Systems” held at the National University of Singapore's Institute for Mathematical Sciences from 17 February to 27 March 2010. It guides the reader through two introductory expositions on large Coulomb systems to five of the most important developments in the field: derivation of mean field equations, derivation of effective Hamiltonians, alternative high precision methods in quantum chemistry, modern many-body methods originating from quantum information, and — the most complex — semirelativistic quantum electrodynamics.These introductions are written by leaders in their fields; amongst them are Volker Bach, Rafael Benguria, Thomas Chen, and Jan Philip Solovej. Together, they fill a gap between current textbooks and the vast modern literature on complex quantum systems.

Spectral Theory and Quantum Mechanics

Spectral Theory and Quantum Mechanics
Author: Valter Moretti
Publisher: Springer
Total Pages: 962
Release: 2018-01-30
Genre: Mathematics
ISBN: 331970706X

This book discusses the mathematical foundations of quantum theories. It offers an introductory text on linear functional analysis with a focus on Hilbert spaces, highlighting the spectral theory features that are relevant in physics. After exploring physical phenomenology, it then turns its attention to the formal and logical aspects of the theory. Further, this Second Edition collects in one volume a number of useful rigorous results on the mathematical structure of quantum mechanics focusing in particular on von Neumann algebras, Superselection rules, the various notions of Quantum Symmetry and Symmetry Groups, and including a number of fundamental results on the algebraic formulation of quantum theories. Intended for Master's and PhD students, both in physics and mathematics, the material is designed to be self-contained: it includes a summary of point-set topology and abstract measure theory, together with an appendix on differential geometry. The book also benefits established researchers by organizing and presenting the profusion of advanced material disseminated in the literature. Most chapters are accompanied by exercises, many of which are solved explicitly."