Path Integrals Hyperbolic Spaces And Selberg Trace Formulae 2nd Edition
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Path Integrals Hyperbolic Spaces And Selberg Trace Formulae
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Author : Christian Grosche
language : en
Publisher: World Scientific
Release Date : 2013
Path Integrals Hyperbolic Spaces And Selberg Trace Formulae written by Christian Grosche and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Mathematics categories.
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.
Path Integrals Hyperbolic Spaces And Selberg Trace Formulae 2nd Edition
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Author : Christian Grosche
language : en
Publisher: World Scientific
Release Date : 2013-07-26
Path Integrals Hyperbolic Spaces And Selberg Trace Formulae 2nd Edition written by Christian Grosche and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-26 with Science categories.
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.
Quantum And Stochastic Mathematical Physics
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Author : Astrid Hilbert
language : en
Publisher: Springer Nature
Release Date : 2023-04-02
Quantum And Stochastic Mathematical Physics written by Astrid Hilbert and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-02 with Mathematics categories.
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.
Mathematical Theory Of Feynman Path Integrals
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Author : Sergio Albeverio
language : en
Publisher: Springer
Release Date : 2008-05-06
Mathematical Theory Of Feynman Path Integrals written by Sergio Albeverio and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-05-06 with Mathematics categories.
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.
Noncommutative Cosmology
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Author : Marcolli Matilde
language : en
Publisher: World Scientific
Release Date : 2017-12-26
Noncommutative Cosmology written by Marcolli Matilde and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-26 with Science categories.
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. Contents: PrefaceAcknowledgmentsGravity and Matter in Noncommutative GeometryRenormalization Group Flows and Early Universe ModelsCosmic TopologyAlgebro-geometric Models in CosmologyMixmaster CosmologiesThe Spectral Action on Bianchi IX CosmologiesFractal and Multifractal Structures in CosmologyNoncommutative Quantum CosmologyBibliography Readership: Graduate students and researchers in mathematical physics and theoretical cosmology. Keywords: Cosmology;Gravity;Particle Physics;GeometryReview: Key Features: While there are recent books that focus on applications of noncommutative geometry to particle physics models, there is presently no other book that focuses on applications to cosmology
American Book Publishing Record
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Author :
language : en
Publisher:
Release Date : 1996
American Book Publishing Record written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with American literature categories.
Selected Papers On Analysis And Differential Equations
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Author : 野水克己
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Selected Papers On Analysis And Differential Equations written by 野水克己 and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Differential equations, Partial categories.
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.
Handbook Of Feynman Path Integrals
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Author : Christian Grosche
language : en
Publisher: Springer
Release Date : 1998-06-22
Handbook Of Feynman Path Integrals written by Christian Grosche and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-06-22 with Mathematics categories.
The Handbook of Feynman Path Integrals appears just fifty years after Richard Feynman published his pioneering paper in 1948 entitled "Space-Time Approach to Non-Relativistic Quantum Mechanics", in which he introduced his new formulation of quantum mechanics in terms of path integrals. The book presents for the first time a comprehensive table of Feynman path integrals together with an extensive list of references; it will serve the reader as a thorough introduction to the theory of path integrals. As a reference book, it is unique in its scope and will be essential for many physicists, chemists and mathematicians working in different areas of research.
Mathematical Feynman Path Integrals And Their Applications
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Author : Sonia Mazzucchi
language : en
Publisher: World Scientific
Release Date : 2009
Mathematical Feynman Path Integrals And Their Applications written by Sonia Mazzucchi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
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.
Path Integrals For Pedestrians
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Author : Ennio Gozzi
language : en
Publisher: World Scientific Publishing Company
Release Date : 2015-11-18
Path Integrals For Pedestrians written by Ennio Gozzi and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-18 with Science categories.
This book aims to provide a quick pedagogical introduction to path integrals. It contains original material that never before has appeared in a book, for example the path integrals for the Wigner functions and for Classical Mechanics. This application to Classical Mechanics connects different fields like Hamiltonian mechanics and differential geometry, so the book is suitable for students and researchers from various disciplines.