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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.
Book Synopsis Path Integrals for Pedestrians by : Ennio Gozzi
Download or read book Path Integrals for Pedestrians written by Ennio Gozzi and published by World Scientific Publishing Company. This book was released on 2015-11-18 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Path Integrals for Pedestrians by : Ennio Gozzi
Download or read book Path Integrals for Pedestrians written by Ennio Gozzi and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
This monograph distills material prepared by the author for class lectures, conferences and research seminars. It fills in a much-felt gap between the older and original work by Feynman and Hibbs and the more recent and advanced volume by Schulman. After presenting an elementary account on the Wiener path integral as applied to Brownian motion, the author progresses on to the statistics of polymers and polymer entanglements. The next three chapters provide an introduction to quantum statistical physics with emphasis on the conceptual understanding of many-variable systems. A chapter on the renormalization group provides material for starting on research work. The final chapter contains an over view of the role of path integrals in recent developments in physics. A good bibliography is provided for each chapter.
Book Synopsis Introduction to Path-integral Methods in Physics and Polymer Science by : Frederik W. Wiegel
Download or read book Introduction to Path-integral Methods in Physics and Polymer Science written by Frederik W. Wiegel and published by World Scientific. This book was released on 1986 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph distills material prepared by the author for class lectures, conferences and research seminars. It fills in a much-felt gap between the older and original work by Feynman and Hibbs and the more recent and advanced volume by Schulman. After presenting an elementary account on the Wiener path integral as applied to Brownian motion, the author progresses on to the statistics of polymers and polymer entanglements. The next three chapters provide an introduction to quantum statistical physics with emphasis on the conceptual understanding of many-variable systems. A chapter on the renormalization group provides material for starting on research work. The final chapter contains an over view of the role of path integrals in recent developments in physics. A good bibliography is provided for each chapter.
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.
Book Synopsis Path Integrals, Hyperbolic Spaces And Selberg Trace Formulae by : Christian Grosche
Download or read book Path Integrals, Hyperbolic Spaces And Selberg Trace Formulae written by Christian Grosche and published by World Scientific. This book was released on 1996-02-29 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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
Book Synopsis Path Integrals on Group Manifolds by : Wolfgang Tomé
Download or read book Path Integrals on Group Manifolds written by Wolfgang Tomé and published by World Scientific. This book was released on 1998-03-31 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
This book, addressing both researchers and graduate students, reviews equivariant localization techniques for the evaluation of Feynman path integrals. The author gives the relevant mathematical background in some detail, showing at the same time how localization ideas are related to classical integrability. The text explores the symmetries inherent in localizable models for assessing the applicability of localization formulae. Various applications from physics and mathematics are presented.
Book Synopsis Equivariant Cohomology and Localization of Path Integrals by : Richard J. Szabo
Download or read book Equivariant Cohomology and Localization of Path Integrals written by Richard J. Szabo and published by Springer Science & Business Media. This book was released on 2003-07-01 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, addressing both researchers and graduate students, reviews equivariant localization techniques for the evaluation of Feynman path integrals. The author gives the relevant mathematical background in some detail, showing at the same time how localization ideas are related to classical integrability. The text explores the symmetries inherent in localizable models for assessing the applicability of localization formulae. Various applications from physics and mathematics are presented.
Providing a pedagogical introduction to the essential principles of path integrals and Hamiltonians, this book describes cutting-edge quantum mathematical techniques applicable to a vast range of fields, from quantum mechanics, solid state physics, statistical mechanics, quantum field theory, and superstring theory to financial modeling, polymers, biology, chemistry, and quantum finance. Eschewing use of the Schrödinger equation, the powerful and flexible combination of Hamiltonian operators and path integrals is used to study a range of different quantum and classical random systems, succinctly demonstrating the interplay between a system's path integral, state space, and Hamiltonian. With a practical emphasis on the methodological and mathematical aspects of each derivation, this is a perfect introduction to these versatile mathematical methods, suitable for researchers and graduate students in physics and engineering.
Book Synopsis Path Integrals and Hamiltonians by : Belal E. Baaquie
Download or read book Path Integrals and Hamiltonians written by Belal E. Baaquie and published by Cambridge University Press. This book was released on 2014-03-27 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing a pedagogical introduction to the essential principles of path integrals and Hamiltonians, this book describes cutting-edge quantum mathematical techniques applicable to a vast range of fields, from quantum mechanics, solid state physics, statistical mechanics, quantum field theory, and superstring theory to financial modeling, polymers, biology, chemistry, and quantum finance. Eschewing use of the Schrödinger equation, the powerful and flexible combination of Hamiltonian operators and path integrals is used to study a range of different quantum and classical random systems, succinctly demonstrating the interplay between a system's path integral, state space, and Hamiltonian. With a practical emphasis on the methodological and mathematical aspects of each derivation, this is a perfect introduction to these versatile mathematical methods, suitable for researchers and graduate students in physics and engineering.
This book on complexity science comprises a collection of chapters on methods and principles from a wide variety of disciplinary fields — from physics and chemistry to biology and the social sciences.In this two-part volume, the first part is a collection of chapters introducing different aspects in a coherent fashion, and providing a common basis and the founding principles of the different complexity science approaches; the next provides deeper discussions of the different methods of use in complexity science, with interesting illustrative applications.The fundamental topics deal with self-organization, pattern formation, forecasting uncertainties, synchronization and revolutionary change, self-adapting and self-correcting systems, and complex networks. Examples are taken from biology, chemistry, engineering, epidemiology, robotics, economics, sociology, and neurology.
Book Synopsis Complexity Science: An Introduction by : Peletier Mark A
Download or read book Complexity Science: An Introduction written by Peletier Mark A and published by World Scientific. This book was released on 2019-03-20 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book on complexity science comprises a collection of chapters on methods and principles from a wide variety of disciplinary fields — from physics and chemistry to biology and the social sciences.In this two-part volume, the first part is a collection of chapters introducing different aspects in a coherent fashion, and providing a common basis and the founding principles of the different complexity science approaches; the next provides deeper discussions of the different methods of use in complexity science, with interesting illustrative applications.The fundamental topics deal with self-organization, pattern formation, forecasting uncertainties, synchronization and revolutionary change, self-adapting and self-correcting systems, and complex networks. Examples are taken from biology, chemistry, engineering, epidemiology, robotics, economics, sociology, and neurology.
This text takes advantage of recent developments in the theory of path integration and attempts to make a major paradigm shift in how the art of functional integration is practiced. The techniques developed in the work will prove valuable to graduate students and researchers in physics, chemistry, mathematical physics, and applied mathematics who find it necessary to deal with solutions to wave equations, both quantum and beyond. A Modern Approach to Functional Integration offers insight into a number of contemporary research topics, which may lead to improved methods and results that cannot be found elsewhere in the textbook literature. Exercises are included in most chapters, making the book suitable for a one-semester graduate course on functional integration.
Book Synopsis A Modern Approach to Functional Integration by : John R. Klauder
Download or read book A Modern Approach to Functional Integration written by John R. Klauder and published by Springer Science & Business Media. This book was released on 2010-11-08 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text takes advantage of recent developments in the theory of path integration and attempts to make a major paradigm shift in how the art of functional integration is practiced. The techniques developed in the work will prove valuable to graduate students and researchers in physics, chemistry, mathematical physics, and applied mathematics who find it necessary to deal with solutions to wave equations, both quantum and beyond. A Modern Approach to Functional Integration offers insight into a number of contemporary research topics, which may lead to improved methods and results that cannot be found elsewhere in the textbook literature. Exercises are included in most chapters, making the book suitable for a one-semester graduate course on functional integration.
Book Synopsis Path Integral Methods and Their Applications by : K. V. Bhagwat
Download or read book Path Integral Methods and Their Applications written by K. V. Bhagwat and published by . This book was released on 1993 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt:
