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BOOK EXCERPT:
This volume presents various aspects of the geometry of symplectic and Poisson manifolds, and applications in Hamiltonian mechanics and geometric quantization are indicated. Chapter 1 presents some general facts about symplectic vector space, symplectic manifolds and symplectic reduction. Chapter 2 deals with the study of Hamiltonian mechanics. Chapter 3 considers some standard facts concerning Lie groups and algebras which lead to the theory of momentum mappings and the Marsden--Weinstein reduction. Chapters 4 and 5 consider the theory and the stability of equilibrium solutions of Hamilton--Poisson mechanical systems. Chapters 6 and 7 are devoted to the theory of geometric quantization. This leads, in Chapter 8, to topics such as foliated cohomology, the theory of the Dolbeault--Kostant complex, and their applications. A discussion of the relation between geometric quantization and the Marsden--Weinstein reduction is presented in Chapter 9. The final chapter considers extending the theory of geometric quantization to Poisson manifolds, via the theory of symplectic groupoids. Each chapter concludes with problems and solutions, many of which present significant applications and, in some cases, major theorems. For graduate students and researchers whose interests and work involve symplectic geometry and Hamiltonian mechanics.
Product Details :
Genre |
: Mathematics |
Author |
: Mircea Puta |
Publisher |
: Springer Science & Business Media |
Release |
: 2012-12-06 |
File |
: 289 Pages |
ISBN-13 |
: 9789401119924 |
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BOOK EXCERPT:
Toric topology is the study of algebraic, differential, symplectic-geometric, combinatorial, and homotopy-theoretic aspects of a particular class of torus actions whose quotients are highly structured. The combinatorial properties of this quotient and the equivariant topology of the original manifold interact in a rich variety of ways, thus illuminating subtle aspects of both the combinatorics and the equivariant topology. Many of the motivations and guiding principles of the fieldare provided by (though not limited to) the theory of toric varieties in algebraic geometry as well as that of symplectic toric manifolds in symplectic geometry.This volume is the proceedings of the International Conference on Toric Topology held in Osaka in May-June 2006. It contains about 25 research and survey articles written by conference speakers, covering many different aspects of, and approaches to, torus actions, such as those mentioned above. Some of the manuscripts are survey articles, intended to give a broad overview of an aspect of the subject; all manuscripts consciously aim to be accessible to a broad reading audience of students andresearchers interested in the interaction of the subjects involved. We hope that this volume serves as an enticing invitation to this emerging field.
Product Details :
Genre |
: Mathematics |
Author |
: Megumi Harada |
Publisher |
: American Mathematical Soc. |
Release |
: 2008 |
File |
: 424 Pages |
ISBN-13 |
: 9780821844861 |
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BOOK EXCERPT:
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.
Product Details :
Genre |
: Mathematics |
Author |
: Denis L. Blackmore |
Publisher |
: World Scientific |
Release |
: 2011 |
File |
: 563 Pages |
ISBN-13 |
: 9789814327152 |
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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.
Product Details :
Genre |
: Science |
Author |
: Luigi Mangiarotti |
Publisher |
: World Scientific |
Release |
: 2005-01-27 |
File |
: 715 Pages |
ISBN-13 |
: 9789814481144 |
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BOOK EXCERPT:
The geometric formulation of autonomous Hamiltonian mechanics in the terms of symplectic and Poisson manifolds is generally accepted. This book provides the geometric formulation of non-autonomous mechanics in a general setting of time-dependent coordinate and reference frame transformations.
Product Details :
Genre |
: Science |
Author |
: G. Giachetta |
Publisher |
: World Scientific |
Release |
: 2011 |
File |
: 405 Pages |
ISBN-13 |
: 9789814313728 |
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BOOK EXCERPT:
Introduction -- Technical preliminaries: tensors, actions and functors -- Applied manifold geometry -- Applied bundle geometry -- Applied jet geometry -- Geometrical path integrals and their applications
Product Details :
Genre |
: Geometry |
Author |
: Vladimir G. Ivancevic |
Publisher |
: World Scientific |
Release |
: 2007 |
File |
: 1346 Pages |
ISBN-13 |
: 9789812770721 |
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BOOK EXCERPT:
This graduate-level monographic textbook treats applied differential geometry from a modern scientific perspective. Co-authored by the originator of the world's leading human motion simulator — “Human Biodynamics Engine”, a complex, 264-DOF bio-mechanical system, modeled by differential-geometric tools — this is the first book that combines modern differential geometry with a wide spectrum of applications, from modern mechanics and physics, via nonlinear control, to biology and human sciences. The book is designed for a two-semester course, which gives mathematicians a variety of applications for their theory and physicists, as well as other scientists and engineers, a strong theory underlying their models.
Product Details :
Genre |
: Mathematics |
Author |
: Vladimir G Ivancevic |
Publisher |
: World Scientific |
Release |
: 2007-05-21 |
File |
: 1346 Pages |
ISBN-13 |
: 9789814475648 |
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BOOK EXCERPT:
This text is part of a two-volume monograph which obtains fundamental notions and results of the standard differential geometry of smooth manifolds, without using differential calculus. Here, the sheaf-theoretic character is emphasized. This has theoretical advantages such as greater perspective, clarity and unification, but also practical benefits ranging from elementary particle physics, via gauge theories and theoretical cosmology (differential spaces), to non-linear PDEs (generalized functions). Thus, more general applications, which are no longer smooth in the classical sense, can be coped with. The treatise might also be construed as a new systematic endeavour to confront the ever-increasing notion that the world around us is far from being smooth enough.
Product Details :
Genre |
: Mathematics |
Author |
: Anastasios Mallios |
Publisher |
: Springer Science & Business Media |
Release |
: 1998 |
File |
: 468 Pages |
ISBN-13 |
: 0792350049 |
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BOOK EXCERPT:
Proceedings of the Colloquium on Differential Geometry, Debrecen, Hungary, July 26-30, 1994
Product Details :
Genre |
: Mathematics |
Author |
: L. Tamássy |
Publisher |
: Springer Science & Business Media |
Release |
: 2012-12-06 |
File |
: 427 Pages |
ISBN-13 |
: 9789400901490 |
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BOOK EXCERPT:
This is a unique 21st-century monograph that reveals a basic, yet deep understanding of the universe, as well as the human mind and body OCo all from the perspective of quantum mechanics and quantum field theory.This book starts with both non-mathematical and mathematical preliminaries. It presents the basics of both non-relativistic and relativistic quantum mechanics, and introduces Feynman path integrals and their application to quantum fields and string theory, as well as some non-quantum applications. It then describes the quantum universe in the form of loop quantum gravity and quantum cosmology. Lastly, the book turns to the human body and mind, applying quantum theory to electro-muscular stimulation and consciousness.It can be used as a graduate (or advanced undergraduate) textbook for a two-semester course in quantum physics and its modern applications. Some parts of the book can also be used by engineers, biologists, psychologists and computer scientists, as well as applied mathematicians, both in industry and academia."
Product Details :
Genre |
: Science |
Author |
: Vladimir G. Ivancevic |
Publisher |
: World Scientific |
Release |
: 2008 |
File |
: 855 Pages |
ISBN-13 |
: 9789812819284 |