Geometric Formulation Of Classical And Quantum Mechanics
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Geometric Formulation Of Classical And Quantum Mechanics
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Author : G. Giachetta
language : en
Publisher: World Scientific
Release Date : 2011
Geometric Formulation Of Classical And Quantum Mechanics written by G. Giachetta and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Science categories.
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.
Geometric Formulation Of Classical And Quantum Mechanics
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Author : Giovanni Giachetta
language : en
Publisher: World Scientific
Release Date : 2010-10-11
Geometric Formulation Of Classical And Quantum Mechanics written by Giovanni Giachetta and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-11 with Science categories.
The geometric formulation of autonomous Hamiltonian mechanics in the terms of symplectic and Poisson manifolds is generally accepted. The literature on this subject is extensive. The present book provides the geometric formulation of non-autonomous mechanics in a general setting of time-dependent coordinate and reference frame transformations. This formulation of mechanics as like as that of classical field theory lies in the framework of general theory of dynamic systems, and Lagrangian and Hamiltonian formalisms on fiber bundles. The reader will find a strict mathematical exposition of non-autonomous dynamic systems, Lagrangian and Hamiltonian non-relativistic mechanics, relativistic mechanics, quantum non-autonomous mechanics, together with a number of advanced models — superintegrable systems, non-autonomous constrained systems, theory of Jacobi fields, mechanical systems with time-dependent parameters, non-adiabatic Berry phase theory, instantwise quantization, and quantization relative to different reference frames.
Geometric Phases In Classical And Quantum Mechanics
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Author : Dariusz Chruscinski
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-06-15
Geometric Phases In Classical And Quantum Mechanics written by Dariusz Chruscinski and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-06-15 with Mathematics categories.
Several well-established geometric and topological methods are used in this work in an application to a beautiful physical phenomenon known as the geometric phase. This book examines the geometric phase, bringing together different physical phenomena under a unified mathematical scheme. The material is presented so that graduate students and researchers in applied mathematics and physics with an understanding of classical and quantum mechanics can handle the text.
Quantum Physics And Geometry
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Author : Edoardo Ballico
language : en
Publisher: Springer
Release Date : 2019-03-13
Quantum Physics And Geometry written by Edoardo Ballico and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-13 with Computers categories.
This book collects independent contributions on current developments in quantum information theory, a very interdisciplinary field at the intersection of physics, computer science and mathematics. Making intense use of the most advanced concepts from each discipline, the authors give in each contribution pedagogical introductions to the main concepts underlying their present research and present a personal perspective on some of the most exciting open problems. Keeping this diverse audience in mind, special efforts have been made to ensure that the basic concepts underlying quantum information are covered in an understandable way for mathematical readers, who can find there new open challenges for their research. At the same time, the volume can also be of use to physicists wishing to learn advanced mathematical tools, especially of differential and algebraic geometric nature.
Geometry And Quantum Field Theory
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Author : Daniel S. Freed
language : en
Publisher: American Mathematical Soc.
Release Date : 1995
Geometry And Quantum Field Theory written by Daniel S. Freed 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 1995 with Mathematics categories.
Exploring topics from classical and quantum mechnanics and field theory, this book is based on lectures presented in the Graduate Summer School at the Regional Geometry Institute in Park City, Utah, in 1991. The chapter by Bryant treats Lie groups and symplectic geometry, examining not only the connection with mechanics but also the application to differential equations and the recent work of the Gromov school. Rabin's discussion of quantum mechanics and field theory is specifically aimed at mathematicians. Alvarez describes the application of supersymmetry to prove the Atiyah-Singer index theorem, touching on ideas that also underlie more complicated applications of supersymmetry. Quinn's account of the topological quantum field theory captures the formal aspects of the path integral and shows how these ideas can influence branches of mathematics which at first glance may not seem connected. Presenting material at a level between that of textbooks and research papers, much of the book would provide excellent material for graduate courses. The book provides an entree into a field that promises to remain exciting and important for years to come.
Geometric Quantization
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Author : Nicholas Michael John Woodhouse
language : en
Publisher: Oxford University Press
Release Date : 1992
Geometric Quantization written by Nicholas Michael John Woodhouse and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.
This book presents a survey of the geometric quantization theory of Kostant and Souriau and was first published in 1980. It has been extensively rewritten and brought up to date, with the addition of many new examples.
Geometric Methods In System Theory
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Author : D.Q. Mayne
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Geometric Methods In System Theory written by D.Q. Mayne and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
Geometric Methods in System Theory In automatic control there are a large number of applications of a fairly simple type for which the motion of the state variables is not free to evolve in a vector space but rather must satisfy some constraints. Examples are numerous; in a switched, lossless electrical network energy is conserved and the state evolves on an ellipsoid surface defined by x'Qx equals a constant; in the control of finite state, continuous time, Markov processes the state evolves on the set x'x = 1, xi ~ O. The control of rigid body motions and trajectory control leads to problems of this type. There has been under way now for some time an effort to build up enough control theory to enable one to treat these problems in a more or less routine way. It is important to emphasise that the ordinary vector space-linear theory often gives the wrong insight and thus should not be relied upon.
Coherent States And Their Applications
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Author : Jean-Pierre Antoine
language : en
Publisher: Springer
Release Date : 2018-06-01
Coherent States And Their Applications written by Jean-Pierre Antoine and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-01 with Science categories.
Coherent states (CS) were originally introduced in 1926 by Schrödinger and rediscovered in the early 1960s in the context of laser physics. Since then, they have evolved into an extremely rich domain that pervades virtually every corner of physics, and have also given rise to a range of research topics in mathematics. The purpose of the 2016 CIRM conference was to bring together leading experts in the field with scientists interested in related topics, to jointly investigate their applications in physics, their various mathematical properties, and their generalizations in many directions. Instead of traditional proceedings, this book presents sixteen longer review-type contributions, which are the outcome of a collaborative effort by many conference participants, subsequently reviewed by independent experts. The book aptly illustrates the diversity of CS aspects, from purely mathematical topics to physical applications, including quantum gravity.
Quantum Geometry
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Author : Margaret Prugovecki
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Quantum Geometry written by Margaret Prugovecki and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Science categories.
This monograph presents a review and analysis of the main mathematical, physical and epistomological difficulties encountered at the foundational level by all the conventional formulations of relativistic quantum theories, ranging from relativistic quantum mechanics and quantum field theory in Minkowski space, to the various canonical and covariant approaches to quantum gravity. It is, however, primarily devoted to the systematic presentation of a quantum framework meant to deal effectively with these difficulties by reconsidering the foundations of these subjects, analyzing their epistemic nature, and then developing mathematical tools which are specifically designed for the elimination of all the basic inconsistencies. A carefully documented historical survey is included, and additional extensive notes containing quotations from original sources are incorporated at the end of each chapter, so that the reader will be brought up-to-date with the very latest developments in quantum field theory in curved spacetime, quantum gravity and quantum cosmology. The survey further provides a backdrop against which the new foundational and mathematical ideas of the present approach to these subjects can be brought out in sharper relief.
Geometric Methods In Physics Xxxvii
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Author : Piotr Kielanowski
language : en
Publisher: Springer Nature
Release Date : 2019-11-26
Geometric Methods In Physics Xxxvii written by Piotr Kielanowski and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-26 with Mathematics categories.
The book consists of articles based on the XXXVII Białowieża Workshop on Geometric Methods in Physics, 2018. The series of Białowieża workshops, attended by a community of experts at the crossroads of mathematics and physics, is a major annual event in the field. This edition of the workshop featured a special session dedicated to Professor Daniel Sternheimer on the occasion of his 80th birthday. The previously unpublished papers present cutting-edge current research, typically grounded in geometry and analysis, with applications to classical and quantum physics. For the past seven years, the Białowieża Workshops have been complemented by a School on Geometry and Physics comprising a series of advanced lectures for graduate students and early-career researchers. The book also includes abstracts of the five lecture series that were given at the seventh school.