Menu Close

Path Integrals Hyperbolic Spaces And Selberg Trace Formulae

These are the books for those you who looking for to read the Path Integrals Hyperbolic Spaces And Selberg Trace Formulae, try to read or download Pdf/ePub books and some of authors may have disable the live reading. Check the book if it available for your country and user who already subscribe will have full access all free books from the library source.

Path Integrals, Hyperbolic Spaces, and Selberg Trace Formulae

Path Integrals Hyperbolic Spaces And Selberg Trace Formulae [Pdf/ePub] eBook

Path Integrals, Hyperbolic Spaces, and Selberg Trace Formulae by Christian Grosche Book Summary:

In this volume, a comprehensive review is given for path integration in two- and three-dimensional homogeneous spaces of constant curvature, including an enumeration of all 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. In addition, an overview is presented on some recent achievements in the theory of the Selberg trace formula on Riemann surfaces, its super generalization, and their use in mathematical physics and quantum chaos. The volume also contains results on the study of the properties of a particular integrable billiard system in the hyperbolic plane, a proposal concerning interbasis expansions for spheroidal coordinate systems in four-dimensional Euclidean space, and some further results derived from the Selberg (super-) trace formula.

Path Integrals, Hyperbolic Spaces and Selberg Trace Formulae

Path Integrals Hyperbolic Spaces And Selberg Trace Formulae [Pdf/ePub] eBook

Path Integrals, Hyperbolic Spaces and Selberg Trace Formulae by Christian Grosche Book Summary:

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 on Group Manifolds

Path Integrals Hyperbolic Spaces And Selberg Trace Formulae [Pdf/ePub] eBook

Path Integrals on Group Manifolds by Wolfgang Tomé Book Summary:

The quantization of physical systems moving on group and symmetric spaces has been an area of active research over the past three decades. This book shows that it is possible to introduce a representation-independent propagator for a real, separable, connected and simply connected Lie group with irreducible, square-integrable representations. For a given set of kinematical variables this propagator is a single generalized function independent of any particular choice of fiducial vector and the irreducible representations of the Lie group generated by these kinematical variables, which nonetheless correctly propagates each element of a continuous representation based on the coherent states associated with these kinematical variables. Furthermore, the book shows that it is possible to construct regularized lattice phase space path integrals for a real, separable, connected and simply connected Lie group with irreducible, square-integrable representations, and although the configuration space is in general a multidimensional curved manifold, it is shown that the resulting lattice phase space path integral has the form of a lattice phase space path integral on a multidimensional flat manifold. Hence, a novel and extremely natural phase space path integral quantization is obtained for general physical systems whose kinematical variables are the generators of a connected and simply connected Lie group. This novel phase space path integral quantization is (a) exact, (b) more general than, and (c) free from the limitations of the previously considered path integral quantizations of free physical systems moving on group manifolds. To illustrate the general theory, a representation-independent propagator is explicitly constructed for SU(2) and the affine group. Contents:Mathematical PreludePhysical PreludeA Review of Some Means to Define Path Integrals on Group and Symmetric SpacesNotations and PreliminariesThe Representation Independent Propagator for a General Lie GroupClassical Limit of the Representation Independent PropagatorConclusion and OutlookContinuous Representation TheoryExact Lattice Calculations Readership: Physicists. Keywords:Global Analysis;Analysis on Manifolds [For Geometric Integration Theory];Spaces and Manifolds of Mappings;Quantum Mechanics (Feynman Path Integrals), Relativity, Fluid Dynamics;Quantum Theory;General Quantum Mechanics and Problems of Quantization;Path IntegralsReviews: “The author explains the theory clearly and the book is almost self-contained …” Contemporary Physics

Handbook of Feynman Path Integrals

Path Integrals Hyperbolic Spaces And Selberg Trace Formulae [Pdf/ePub] eBook

Handbook of Feynman Path Integrals by Christian Grosche,Frank Steiner Book Summary:

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.

Turkish Journal of Physics

Path Integrals Hyperbolic Spaces And Selberg Trace Formulae [Pdf/ePub] eBook

Turkish Journal of Physics by N.A Book Summary:

Download or read Turkish Journal of Physics book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc).

Government Reports Announcements & Index

Path Integrals Hyperbolic Spaces And Selberg Trace Formulae [Pdf/ePub] eBook

Government Reports Announcements & Index by N.A Book Summary:

Download or read Government Reports Announcements & Index book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc).

Infinite Dimensional Stochastic Analysis

Path Integrals Hyperbolic Spaces And Selberg Trace Formulae [Pdf/ePub] eBook

Infinite Dimensional Stochastic Analysis by Philippe Clément Book Summary:

Download or read Infinite Dimensional Stochastic Analysis book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc).

INIS Atomindex

Path Integrals Hyperbolic Spaces And Selberg Trace Formulae [Pdf/ePub] eBook

INIS Atomindex by N.A Book Summary:

Download or read INIS Atomindex book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc).

American Book Publishing Record

Path Integrals Hyperbolic Spaces And Selberg Trace Formulae [Pdf/ePub] eBook

American Book Publishing Record by N.A Book Summary:

Download or read American Book Publishing Record book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc).

The Cumulative Book Index

Path Integrals Hyperbolic Spaces And Selberg Trace Formulae [Pdf/ePub] eBook

The Cumulative Book Index by N.A Book Summary:

Download or read The Cumulative Book Index book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc).

Mathematical Reviews

Path Integrals Hyperbolic Spaces And Selberg Trace Formulae [Pdf/ePub] eBook

Mathematical Reviews by N.A Book Summary:

Download or read Mathematical Reviews book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc).

Journal of physics : A, Mathematical and general

Path Integrals Hyperbolic Spaces And Selberg Trace Formulae [Pdf/ePub] eBook

Journal of physics : A, Mathematical and general by N.A Book Summary:

Download or read Journal of physics : A, Mathematical and general book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc).

Integrable and Superintegrable Systems

Path Integrals Hyperbolic Spaces And Selberg Trace Formulae [Pdf/ePub] eBook

Integrable and Superintegrable Systems by Boris A Kupershmidt Book Summary:

Some of the most active practitioners in the field of integrable systems have been asked to describe what they think of as the problems and results which seem to be most interesting and important now and are likely to influence future directions. The papers in this collection, representing their authors' responses, offer a broad panorama of the subject as it enters the 1990's. Contents:The Main Soliton Theorem (I Cherednik)Functional Bethe Ansatz (E K Sklyanin)Integrability in Models of Two-Dimensional Turbulence (Y Murometz & S Razboynick)Solitons, Numerical Chaos and Cellular Automata (M J Ablowitz et al.)The Unstable Nonlinear Schrödinger Equation (T Yajima & M Wadati)Classification of Integrable Equations (R K Dodd)List of All Integrable Hamiltonian Systems of General Type with Two Degrees of Freedom (A T Fomenko)Finite-Dimensional Soliton Systems (S N M Ruijsenaars)Relativistic Analogs of Basic Integrable Systems (J Gibbons & B A Kupershmidt)Liouville Generating Functions for Isospectral Flows in Loop Algebras (M R Adams et al.)A Loop Algebra Decomposition for Korteweg-de Vries Equations (R J Schilling)Energy Dependent Spectral Problems: Their Hamiltonian Structures and Miura Maps (A P Fordy)Commuting Differential Operators Over Integrable Hierarchies (F Guil)Lie Superalgebra Structure on Eigenfunctions, and Jets of the Resolvent's Kernal Near the Derivative and the Bott Cocycle (A O Radul)Super Miura Transformations, Super Schwarzian Derivatives and Super Hill Operators (P Mathieu) Readership: Mathematicians and physicists. keywords:

Path Integrals for Stochastic Processes

Path Integrals Hyperbolic Spaces And Selberg Trace Formulae [Pdf/ePub] eBook

Path Integrals for Stochastic Processes by Horacio S. Wio Book Summary:

This book provides an introductory albeit solid presentation of path integration techniques as applied to the field of stochastic processes. The subject began with the work of Wiener during the 1920''s, corresponding to a sum over random trajectories, anticipating by two decades Feynman''s famous work on the path integral representation of quantum mechanics. However, the true trigger for the application of these techniques within nonequilibrium statistical mechanics and stochastic processes was the work of Onsager and Machlup in the early 1950''s. The last quarter of the 20th century has witnessed a growing interest in this technique and its application in several branches of research, even outside physics (for instance, in economy).The aim of this book is to offer a brief but complete presentation of the path integral approach to stochastic processes. It could be used as an advanced textbook for graduate students and even ambitious undergraduates in physics. It describes how to apply these techniques for both Markov and non-Markov processes. The path expansion (or semiclassical approximation) is discussed and adapted to the stochastic context. Also, some examples of nonlinear transformations and some applications are discussed, as well as examples of rather unusual applications. An extensive bibliography is included. The book is detailed enough to capture the interest of the curious reader, and complete enough to provide a solid background to explore the research literature and start exploiting the learned material in real situations.

Power of a Positive Woman

Path Integrals Hyperbolic Spaces And Selberg Trace Formulae [Pdf/ePub] eBook

Power of a Positive Woman by Karol Ladd Book Summary:

This life-changing book explores seven principles that can help you become a powerful force in your family, your church, your community, and your world. Through biblical teaching, inspirational quotes, and true stories of women just like you, you will learn to incorporate your life as you have a powerful impact on those around you. Do you want to be a positive woman of powerful influence? Do you want to make a lasting impression on the lives of the people around you? You can become a positive woman—no matter where you find yourself right now—simply by choosing to allow God's power and strength to pour through you. This life-changing book explores seven principles that can help you become a powerful force in your family, your church, your community, and your world. Through biblical teaching, inspirational quotes, and true stories of women just like you, you will learn to incorporate your life as you have a powerful impact on those around you. Every woman—including you—has the potential to become a positive, powerful influence in her world. Never underestimate the power of a positive woman. That woman can be you!

Nonlinear Dynamical Systems of Mathematical Physics

Path Integrals Hyperbolic Spaces And Selberg Trace Formulae [Pdf/ePub] eBook

Nonlinear Dynamical Systems of Mathematical Physics by Denis L. Blackmore,Anatoli? Karolevich Prikarpatski?,Valeriy Hr Samoylenko Book Summary:

This distinctive volume presents a clear, rigorous grounding in modern nonlinear integrable dynamics theory and applications in mathematical physics, and an introduction to timely leading-edge developments in the field - including some innovations by the authors themselves - that have not appeared in any other book. The exposition begins with an introduction to modern integrable dynamical systems theory, treating such topics as Liouville?Arnold and Mischenko?Fomenko integrability. This sets the stage for such topics as new formulations of the gradient-holonomic algorithm for Lax integrability, novel treatments of classical integration by quadratures, Lie-algebraic characterizations of integrability, and recent results on tensor Poisson structures. Of particular note is the development via spectral reduction of a generalized de Rham?Hodge theory, related to Delsarte-Lions operators, leading to new Chern type classes useful for integrability analysis. Also included are elements of quantum mathematics along with applications to Whitham systems, gauge theories, hadronic string models, and a supplement on fundamental differential-geometric concepts making this volume essentially self-contained. This book is ideal as a reference and guide to new directions in research for advanced students and researchers interested in the modern theory and applications of integrable (especially infinite-dimensional) dynamical systems.

Geometry and Spectra of Compact Riemann Surfaces

Path Integrals Hyperbolic Spaces And Selberg Trace Formulae [Pdf/ePub] eBook

Geometry and Spectra of Compact Riemann Surfaces by Peter Buser Book Summary:

This monograph is a self-contained introduction to the geometry of Riemann Surfaces of constant curvature –1 and their length and eigenvalue spectra. It focuses on two subjects: the geometric theory of compact Riemann surfaces of genus greater than one, and the relationship of the Laplace operator with the geometry of such surfaces. Research workers and graduate students interested in compact Riemann surfaces will find here a number of useful tools and insights to apply to their investigations.

Le spectre des surfaces hyperboliques

Path Integrals Hyperbolic Spaces And Selberg Trace Formulae [Pdf/ePub] eBook

Le spectre des surfaces hyperboliques by Nicolas Bergeron Book Summary:

Cet ouvrage est une introduction a la theorie spectrale du laplacien sur les surfaces hyperboliques (de courbure 1), compactes ou d'aire finie. Pour certaines de ces surfaces, dites - surfaces hyperboliques arithmetiques -, les fonctions propres sont des objets de nature arithmetique et des outils d'analyse sont employes conjointement a des methodes puissantes de theorie des nombres pour les etudier. Apres une introduction a la geometrie hyperbolique des surfaces insistant sur celles qui sont arithmetiques, puis une introduction aux methodes d'analyse spectrale de l'operateur de Laplace sur celles- ci, l'auteur developpe l'analogie geometrie (geodesiques fermees) - arithmetique (nombres premiers) en demontrant la formule des traces de Selberg. Outre des applications importantes a l'arithmetique, l'auteur propose des applications a la statistique spectrale de l'operateur de Laplace et a la propriete d'unique ergodicite quantique (theoreme d'unique ergodicite quantique arithmetique, recemment demontre par Elon Lindenstrauss). L'ouvrage, issu de plusieurs cours de M2 a Orsay et a l'Universite P. & M. Curie, permet au lecteur de parcourir un champ mathematique classique et d'etre conduit vers des domaines de recherche tres actifs.

Integral Equations of First Kind

Path Integrals Hyperbolic Spaces And Selberg Trace Formulae [Pdf/ePub] eBook

Integral Equations of First Kind by A. V. Bitsadze Book Summary:

This book studies classes of linear integral equations of the first kind most often met in applications. Since the general theory of integral equations of the first kind has not been formed yet, the book considers the equations whose solutions either are estimated in quadratures or can be reduced to well-investigated classes of integral equations of the second kind.In this book the theory of integral equations of the first kind is constructed by using the methods of the theory of functions both of real and complex variables. Special attention is paid to the inversion formulas of model equations most often met in physics, mechanics, astrophysics, chemical physics etc. The general theory of linear equations including the Fredholm, the Noether, the Hausdorff theorems, the Hilbert-Schmidt theorem, the Picard theorem and the application of this theory to the solution of boundary problems are given in this book. The book studies the equations of the first kind with the Schwarz Kernel, the Poisson and the Neumann kernels; the Volterra integral equations of the first kind, the Abel equations and some generalizations, one-dimensional and many-dimensional analogues of the Cauchy type integral and some of their applications.

Harmonic Analysis on Symmetric Spaces and Applications II

Path Integrals Hyperbolic Spaces And Selberg Trace Formulae [Pdf/ePub] eBook

Harmonic Analysis on Symmetric Spaces and Applications II by Audrey Terras Book Summary:

Well, finally, here it is-the long-promised "Revenge of the Higher Rank Symmetric Spaces and Their Fundamental Domains." When I began work on it in 1977, I would probably have stopped immediately if someone had told me that ten years would pass before I would declare it "finished." Yes, I am declaring it finished-though certainly not perfected. There is a large amount of work going on at the moment as the piles of preprints reach the ceiling. Nevertheless, it is summer and the ocean calls. So I am not going to spend another ten years revising and polishing. But, gentle reader, do send me your corrections and even your preprints. Thanks to your work, there is an Appendix at the end of this volume with corrections to Volume I. I said it all in the Preface to Volume I. So I will try not to repeat myself here. Yes, the "recent trends" mentioned in that Preface are still just as recent.