Download or read book Mechanics Analysis and Geometry 200 Years after Lagrange written by M. Francaviglia and published by Elsevier. This book was released on 2012-12-02 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing a logically balanced and authoritative account of the different branches and problems of mathematical physics that Lagrange studied and developed, this volume presents up-to-date developments in differential goemetry, dynamical systems, the calculus of variations, and celestial and analytical mechanics.
Download or read book Gauge Mechanics written by Luigi Mangiarotti and published by World Scientific. This book was released on 1998-12-07 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents in a unified way modern geometric methods in analytical mechanics based on the application of fibre bundles, jet manifold formalism and the related concept of connection. Non-relativistic mechanics is seen as a particular field theory over a one-dimensional base. In fact, the concept of connection is the major link throughout the book. In the gauge scheme of mechanics, connections appear as reference frames, dynamic equations, and in Lagrangian and Hamiltonian formalisms. Inertial forces, energy conservation laws and other phenomena related to reference frames are analyzed; that leads us to observable physics. Special topics on relativistic mechanics, geometric BRST mechanics frame-dependent quantization and others, together with many examples, are also dealt with.
Download or read book Symplectic Geometry and Mathematical Physics written by P. Donato and published by Springer Science & Business Media. This book was released on 1991-12 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the conference "Colloque de Goometrie Symplectique et Physique Mathematique" which was held in Aix-en-Provence (France), June 11-15, 1990, in honor of Jean-Marie Souriau. The conference was one in the series of international meetings of the Seminaire Sud Rhodanien de Goometrie, an organization of geometers and mathematical physicists at the Universities of Avignon, Lyon, Mar seille, and Montpellier. The scientific interests of Souriau, one of the founders of geometric quantization, range from classical mechanics (symplectic geometry) and quantization problems to general relativity and astrophysics. The themes of this conference cover "only" the first two of these four areas. The subjects treated in this volume could be classified in the follow ing way: symplectic and Poisson geometry (Arms-Wilbour, Bloch-Ratiu, Brylinski-Kostant, Cushman-Sjamaar, Dufour, Lichnerowicz, Medina, Ouzilou), classical mechanics (Benenti, Holm-Marsden, Marle) , particles and fields in physics (Garcia Perez-Munoz Masque, Gotay, Montgomery, Ne'eman-Sternberg, Sniatycki) and quantization (Blattner, Huebschmann, Karasev, Rawnsley, Roger, Rosso, Weinstein). However, these subjects are so interrelated that a classification by headings such as "pure differential geometry, applications of Lie groups, constrained systems in physics, etc. ," would have produced a completely different clustering! The list of authors is not quite identical to the list of speakers at the conference. M. Karasev was invited but unable to attend; C. Itzykson and M. Vergne spoke on work which is represented here only by the title of Itzykson's talk (Surfaces triangulees et integration matricielle) and a summary of Vergne's talk.
Download or read book Mathematical Aspects of Classical Field Theory written by Mark J. Gotay and published by American Mathematical Soc.. This book was released on 1992 with total page 658 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classical field theory has undergone a renaissance in recent years. Symplectic techniques have yielded deep insights into its foundations, as has an improved understanding of the variational calculus. Further impetus for the study of classical fields has come from other areas, such as integrable systems, Poisson geometry, global analysis, and quantum theory. This book contains the proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Mathematical Aspects of Classical Field Theory, held in July 1991 at the University of Washington at Seattle. The conference brought together researchers in many of the main areas of classical field theory to present the latest ideas and results. The volume contains thirty refereed papers, both survey and research articles, and is designed to reflect the state of the art as well as chart the future course of the subject. The topics fall into four major categories: global analysis and relativity (cosmic censorship, initial value problem, quantum gravity), geometric methods (symplectic and Poisson structures, momentum mappings, Dirac constraint theory), BRST theory, and the calculus of variations (the variational bicomplex, higher order theories). Also included are related topics with a ``classical basis'', such as geometric quantization, integrable systems, symmetries, deformation theory, and geometric mechanics.
Download or read book Philosophy of Physics written by Jeremy Butterfield and published by Elsevier. This book was released on 2007 with total page 1481 pages. Available in PDF, EPUB and Kindle. Book excerpt: The ambition of this volume is twofold: to provide a comprehensive overview of the field and to serve as an indispensable reference work for anyone who wants to work in it. For example, any philosopher who hopes to make a contribution to the topic of the classical-quantum correspondence will have to begin by consulting Klaas Landsman's chapter. The organization of this volume, as well as the choice of topics, is based on the conviction that the important problems in the philosophy of physics arise from studying the foundations of the fundamental theories of physics. It follows that there is no sharp line to be drawn between philosophy of physics and physics itself. Some of the best work in the philosophy of physics is being done by physicists, as witnessed by the fact that several of the contributors to the volume are theoretical physicists: viz., Ellis, Emch, Harvey, Landsman, Rovelli, 't Hooft, the last of whom is a Nobel laureate. Key features - Definitive discussions of the philosophical implications of modern physics - Masterly expositions of the fundamental theories of modern physics - Covers all three main pillars of modern physics: relativity theory, quantum theory, and thermal physics - Covers the new sciences grown from these theories: for example, cosmology from relativity theory; and quantum information and quantum computing, from quantum theory - Contains special Chapters that address crucial topics that arise in several different theories, such as symmetry and determinism - Written by very distinguished theoretical physicists, including a Nobel Laureate, as well as by philosophers - Definitive discussions of the philosophical implications of modern physics - Masterly expositions of the fundamental theories of modern physics - Covers all three main pillars of modern physics: relativity theory, quantum theory, and thermal physics - Covers the new sciences that have grown from these theories: for example, cosmology from relativity theory; and quantum information and quantum computing, from quantum theory - Contains special Chapters that address crucial topics that arise in several different theories, such as symmetry and determinism - Written by very distinguished theoretical physicists, including a Nobel Laureate, as well as by philosophers
Download or read book Hamiltonian Systems and Celestial Mechanics written by and published by World Scientific. This book was released on 2000 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is an outgrowth of the Third International Symposium on Hamiltonian Systems and Celestial Mechanics. The main topics are Arnold diffusion, central configurations, singularities in few-body problems, billiards, area-preserving maps, and geometrical mechanics. All papers in the volume went through the refereeing process typical of a mathematical research journal.
Download or read book Noether s Theorems written by Gennadi Sardanashvily and published by Springer. This book was released on 2016-03-18 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides a detailed exposition of the calculus of variations on fibre bundles and graded manifolds. It presents applications in such area's as non-relativistic mechanics, gauge theory, gravitation theory and topological field theory with emphasis on energy and energy-momentum conservation laws. Within this general context the first and second Noether theorems are treated in the very general setting of reducible degenerate graded Lagrangian theory.
Download or read book Differential Geometry Riemannian Geometry written by Robert Everist Greene and published by American Mathematical Soc.. This book was released on 1993 with total page 735 pages. Available in PDF, EPUB and Kindle. Book excerpt: The third of three parts comprising Volume 54, the proceedings of the Summer Research Institute on Differential Geometry, held at the University of California, Los Angeles, July 1990 (ISBN for the set is 0-8218-1493-1). Part 3 begins with an overview by R.E. Greene of some recent trends in Riemannia
Download or read book Generalized Hamiltonian Formalism for Field Theory written by G. Sardanashvily and published by World Scientific. This book was released on 1995 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the framework of the geometric formulation of field theory, classical fields are represented by sections of fibred manifolds, and their dynamics is phrased in jet manifold terms. The Hamiltonian formalism in fibred manifolds is the multisymplectic generalization of the Hamiltonian formalism in mechanics when canonical momenta correspond to derivatives of fields with respect to all world coordinates, not only to time. This book is devoted to the application of this formalism to fundamental field models including gauge theory, gravitation theory, and spontaneous symmetry breaking. All these models are constraint ones. Their Euler-Lagrange equations are underdetermined and need additional conditions. In the Hamiltonian formalism, these conditions appear automatically as a part of the Hamilton equations, corresponding to different Hamiltonian forms associated with a degenerate Lagrangian density. The general procedure for describing constraint systems with quadratic and affine Lagrangian densities is presented.
Download or read book Handbook of Differential Equations Evolutionary Equations written by C.M. Dafermos and published by Elsevier. This book was released on 2005-10-05 with total page 677 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this Handbook is to acquaint the reader with the current status of the theory of evolutionary partial differential equations, and with some of its applications. Evolutionary partial differential equations made their first appearance in the 18th century, in the endeavor to understand the motion of fluids and other continuous media. The active research effort over the span of two centuries, combined with the wide variety of physical phenomena that had to be explained, has resulted in an enormous body of literature. Any attempt to produce a comprehensive survey would be futile. The aim here is to collect review articles, written by leading experts, which will highlight the present and expected future directions of development of the field. The emphasis will be on nonlinear equations, which pose the most challenging problems today.. Volume I of this Handbook does focus on the abstract theory of evolutionary equations. . Volume 2 considers more concrete problems relating to specific applications. . Together they provide a panorama of this amazingly complex and rapidly developing branch of mathematics.
Download or read book Quantum Gravity written by Carlo Rovelli and published by Cambridge University Press. This book was released on 2007-11-29 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum gravity is perhaps the most important open problem in fundamental physics. It is the problem of merging quantum mechanics and general relativity, the two great conceptual revolutions in the physics of the twentieth century. The loop and spinfoam approach, presented in this 2004 book, is one of the leading research programs in the field. The first part of the book discusses the reformulation of the basis of classical and quantum Hamiltonian physics required by general relativity. The second part covers the basic technical research directions. Appendices include a detailed history of the subject of quantum gravity, hard-to-find mathematical material, and a discussion of some philosophical issues raised by the subject. This fascinating text is ideal for graduate students entering the field, as well as researchers already working in quantum gravity. It will also appeal to philosophers and other scholars interested in the nature of space and time.
Download or read book Gravity Particles and Space time written by Petr Ivanovich Pronin and published by World Scientific. This book was released on 1996 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume comprises original and review articles on the frontier problems of the gravitation theory, theoretical and mathematical physics. The volume is dedicated to the memory of Professor Dmitri Ivanenko who made the great contribution to the physical science of the twentieth century.
Download or read book Geometric And Algebraic Topological Methods In Quantum Mechanics written by Luigi Mangiarotti and published by World Scientific. This book was released on 2005-01-27 with total page 715 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last decade, the development of new ideas in quantum theory, including geometric and deformation quantization, the non-Abelian Berry's geometric factor, super- and BRST symmetries, non-commutativity, has called into play the geometric techniques based on the deep interplay between algebra, differential geometry and topology. The book aims at being a guide to advanced differential geometric and topological methods in quantum mechanics. Their main peculiarity lies in the fact that geometry in quantum theory speaks mainly the algebraic language of rings, modules, sheaves and categories. Geometry is by no means the primary scope of the book, but it underlies many ideas in modern quantum physics and provides the most advanced schemes of quantization.
Download or read book Accelerating Expansion written by Gordon Belot and published by Oxford University Press. This book was released on 2023-08-24 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: Accelerating Expansion explores some of the philosophical implications of modern cosmology, focused on the significance that the discovery of the accelerating expansion of the Universe has for our understanding of time, geometry, and physics. The appearance of the cosmological constant in the equations of general relativity allows one to model universes in which space has an inherent tendency towards expansion. This constant, introduced by Einstein but subsequently abandoned by him, returned to centre stage with the discovery of the accelerating expansion. This pedagogically-oriented essay begins with a study of the most basic and elegant relativistic world that involves a positive cosmological constant, de Sitter spacetime. It then turns to the relatives of de Sitter spacetime that dominate modern relativistic cosmology. Some of the topics considered include: the nature of time and simultaneity in de Sitter worlds; the sense in which de Sitter spacetime is a powerful dynamical attractor; the limited extent to which observation can give us information about the topology of space in a world undergoing accelerated expansion; and cosmologists' favourite sceptical worry about the reliability of evidence and the possibility of knowledge, the problem of Boltzmann brains.
Download or read book Paradoxes Of Measures And Dimensions Originating In Felix Hausdorff s Ideas written by Janusz Czyz and published by World Scientific. This book was released on 1994-01-14 with total page 767 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, many ideas by Felix Hausdorff are described and contemporary mathematical theories stemming from them are sketched.
Download or read book Modern Mathematical Tools and Techniques in Capturing Complexity written by Leandro Pardo and published by Springer Science & Business Media. This book was released on 2011-05-26 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: Real-life problems are often quite complicated in form and nature and, for centuries, many different mathematical concepts, ideas and tools have been developed to formulate these problems theoretically and then to solve them either exactly or approximately. This book aims to gather a collection of papers dealing with several different problems arising from many disciplines and some modern mathematical approaches to handle them. In this respect, the book offers a wide overview on many of the current trends in Mathematics as valuable formal techniques in capturing and exploiting the complexity involved in real-world situations. Several researchers, colleagues, friends and students of Professor María Luisa Menéndez have contributed to this volume to pay tribute to her and to recognize the diverse contributions she had made to the fields of Mathematics and Statistics and to the profession in general. She had a sweet and strong personality, and instilled great values and work ethics in her students through her dedication to teaching and research. Even though the academic community lost her prematurely, she would continue to provide inspiration to many students and researchers worldwide through her published work.
Download or read book Advanced Classical Field Theory written by Giovanni Giachetta and published by World Scientific. This book was released on 2009-05-04 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contemporary quantum field theory is mainly developed as quantization of classical fields. Therefore, classical field theory and its BRST extension is the necessary step towards quantum field theory. This book aims to provide a complete mathematical foundation of Lagrangian classical field theory and its BRST extension for the purpose of quantization. Based on the standard geometric formulation of theory of nonlinear differential operators, Lagrangian field theory is treated in a very general setting. Reducible degenerate Lagrangian theories of even and odd fields on an arbitrary smooth manifold are considered. The second Noether theorems generalized to these theories and formulated in the homology terms provide the strict mathematical formulation of BRST extended classical field theory. The most physically relevant field theories — gauge theory on principal bundles, gravitation theory on natural bundles, theory of spinor fields and topological field theory — are presented in a complete way.This book is designed for theoreticians and mathematical physicists specializing in field theory. The authors have tried throughout to provide the necessary mathematical background, thus making the exposition self-contained.
