Path Integrals Hyperbolic Spaces And Selberg Trace Formulae 2nd Edition PDF Download
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Author | : Christian Grosche |
Publisher | : World Scientific |
Total Pages | : 389 |
Release | : 2013-07-26 |
Genre | : Science |
ISBN | : 9814460095 |
Download Path Integrals, Hyperbolic Spaces And Selberg Trace Formulae (2nd Edition) Book in PDF, ePub and Kindle
In this second edition, a comprehensive review is given for path integration in two- and three-dimensional (homogeneous) spaces of constant and non-constant curvature, including an enumeration of all the corresponding coordinate systems which allow separation of variables in the Hamiltonian and in the path integral. The corresponding path integral solutions are presented as a tabulation. Proposals concerning interbasis expansions for spheroidal coordinate systems are also given. In particular, the cases of non-constant curvature Darboux spaces are new in this edition.The volume also contains results on the numerical study of the properties of several integrable billiard systems in compact domains (i.e. rectangles, parallelepipeds, circles and spheres) in two- and three-dimensional flat and hyperbolic spaces. In particular, the discussions of integrable billiards in circles and spheres (flat and hyperbolic spaces) and in three dimensions are new in comparison to the first edition.In addition, an overview is presented on some recent achievements in the theory of the Selberg trace formula on Riemann surfaces, its super generalization, their use in mathematical physics and string theory, and some further results derived from the Selberg (super-) trace formula.
Author | : Christian Grosche |
Publisher | : World Scientific |
Total Pages | : 389 |
Release | : 2013 |
Genre | : Mathematics |
ISBN | : 9814460087 |
Download Path Integrals, Hyperbolic Spaces and Selberg Trace Formulae Book in PDF, ePub and Kindle
In this second edition, a comprehensive review is given for path integration in two- and three-dimensional (homogeneous) spaces of constant and non-constant curvature, including an enumeration of all the corresponding coordinate systems which allow separation of variables in the Hamiltonian and in the path integral. The corresponding path integral solutions are presented as a tabulation. Proposals concerning interbasis expansions for spheroidal coordinate systems are also given. In particular, the cases of non-constant curvature Darboux spaces are new in this edition. The volume also contains results on the numerical study of the properties of several integrable billiard systems in compact domains (i.e. rectangles, parallelepipeds, circles and spheres) in two- and three-dimensional flat and hyperbolic spaces. In particular, the discussions of integrable billiards in circles and spheres (flat and hyperbolic spaces) and in three dimensions are new in comparison to the first edition. In addition, an overview is presented on some recent achievements in the theory of the Selberg trace formula on Riemann surfaces, its super generalization, their use in mathematical physics and string theory, and some further results derived from the Selberg (super-) trace formula.
Author | : Astrid Hilbert |
Publisher | : Springer Nature |
Total Pages | : 390 |
Release | : 2023-04-02 |
Genre | : Mathematics |
ISBN | : 3031140311 |
Download Quantum and Stochastic Mathematical Physics Book in PDF, ePub and Kindle
Sergio Albeverio gave important contributions to many fields ranging from Physics to Mathematics, while creating new research areas from their interplay. Some of them are presented in this Volume that grew out of the Random Transformations and Invariance in Stochastic Dynamics Workshop held in Verona in 2019. To understand the theory of thermo- and fluid-dynamics, statistical mechanics, quantum mechanics and quantum field theory, Albeverio and his collaborators developed stochastic theories having strong interplays with operator theory and functional analysis. His contribution to the theory of (non Gaussian)-SPDEs, the related theory of (pseudo-)differential operators, and ergodic theory had several impacts to solve problems related, among other topics, to thermo- and fluid dynamics. His scientific works in the theory of interacting particles and its extension to configuration spaces lead, e.g., to the solution of open problems in statistical mechanics and quantum field theory. Together with Raphael Hoegh Krohn he introduced the theory of infinite dimensional Dirichlet forms, which nowadays is used in many different contexts, and new methods in the theory of Feynman path integration. He did not fear to further develop different methods in Mathematics, like, e.g., the theory of non-standard analysis and p-adic numbers.
Author | : Sergio Albeverio |
Publisher | : Springer Science & Business Media |
Total Pages | : 184 |
Release | : 2008-05-30 |
Genre | : Mathematics |
ISBN | : 3540769544 |
Download Mathematical Theory of Feynman Path Integrals Book in PDF, ePub and Kindle
The 2nd edition of LNM 523 is based on the two first authors' mathematical approach of this theory presented in its 1st edition in 1976. An entire new chapter on the current forefront of research has been added. Except for this new chapter and the correction of a few misprints, the basic material and presentation of the first edition has been maintained. At the end of each chapter the reader will also find notes with further bibliographical information.
Author | : Matilde Marcolli |
Publisher | : World Scientific |
Total Pages | : 292 |
Release | : 2017-12-26 |
Genre | : Science |
ISBN | : 9813202866 |
Download Noncommutative Cosmology Book in PDF, ePub and Kindle
Modified gravity models play an important role in contemporary theoretical cosmology. The present book proposes a novel approach to the topic based on techniques from noncommutative geometry, especially the spectral action functional as a gravity model. The book discusses applications to early universe models and slow-roll inflation models, to the problem of cosmic topology, to non-isotropic cosmologies like mixmaster universes and Bianchi IX gravitational instantons, and to multifractal structures in cosmology.Relations between noncommutative and algebro-geometric methods in cosmology is also discussed, including the occurrence of motives, periods, and modular forms in spectral models of gravity.
Author | : |
Publisher | : |
Total Pages | : 1328 |
Release | : 1996 |
Genre | : American literature |
ISBN | : |
Download American Book Publishing Record Book in PDF, ePub and Kindle
Author | : 野水克己 |
Publisher | : American Mathematical Soc. |
Total Pages | : 152 |
Release | : 2003 |
Genre | : Differential equations, Partial |
ISBN | : 9780821835081 |
Download Selected Papers on Analysis and Differential Equations Book in PDF, ePub and Kindle
This volume contains translations of papers that originally appeared in the Japanese journal, Sugaku. Ordinarily the papers would appear in the AMS translation of that journal, but to expedite publication, the Society has chosen to publish them as a volume of selected papers. The papers range over a variety of topics, including nonlinear partial differential equations, $C*$-algebras, and Schrodinger operators. The volume is suitable for graduate students and research mathematicians interested in analysis and differential equations.
Author | : Sergio Albeverio |
Publisher | : Springer |
Total Pages | : 184 |
Release | : 2008-05-06 |
Genre | : Mathematics |
ISBN | : 3540769560 |
Download Mathematical Theory of Feynman Path Integrals Book in PDF, ePub and Kindle
The 2nd edition of LNM 523 is based on the two first authors' mathematical approach of this theory presented in its 1st edition in 1976. An entire new chapter on the current forefront of research has been added. Except for this new chapter and the correction of a few misprints, the basic material and presentation of the first edition has been maintained. At the end of each chapter the reader will also find notes with further bibliographical information.
Author | : Sonia Mazzucchi |
Publisher | : World Scientific |
Total Pages | : 225 |
Release | : 2009 |
Genre | : Mathematics |
ISBN | : 9812836918 |
Download Mathematical Feynman Path Integrals and Their Applications Book in PDF, ePub and Kindle
Although more than 60 years have passed since their first appearance, Feynman path integrals have yet to lose their fascination and luster. They are not only a formidable instrument of theoretical physics, but also a mathematical challenge; in fact, several mathematicians in the last 40 years have devoted their efforts to the rigorous mathematical definition of Feynman''s ideas. This volume provides a detailed, self-contained description of the mathematical difficulties as well as the possible techniques used to solve these difficulties. In particular, it gives a complete overview of the mathematical realization of Feynman path integrals in terms of well-defined functional integrals, that is, the infinite dimensional oscillatory integrals. It contains the traditional results on the topic as well as the more recent developments obtained by the author. Mathematical Feynman Path Integrals and Their Applications is devoted to both mathematicians and physicists, graduate students and researchers who are interested in the problem of mathematical foundations of Feynman path integrals.
Author | : |
Publisher | : |
Total Pages | : 2312 |
Release | : 1997 |
Genre | : American literature |
ISBN | : |
Download The Cumulative Book Index Book in PDF, ePub and Kindle
A world list of books in the English language.