Geometric Quantization
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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.
Loop Spaces Characteristic Classes And Geometric Quantization
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Author : Jean-Luc Brylinski
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-12-30
Loop Spaces Characteristic Classes And Geometric Quantization written by Jean-Luc Brylinski 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 2009-12-30 with Mathematics categories.
This book examines the differential geometry of manifolds, loop spaces, line bundles and groupoids, and the relations of this geometry to mathematical physics. Applications presented in the book involve anomaly line bundles on loop spaces and anomaly functionals, central extensions of loop groups, Kähler geometry of the space of knots, and Cheeger--Chern--Simons secondary characteristics classes. It also covers the Dirac monopole and Dirac’s quantization of the electrical charge.
Geometric Quantization And Quantum Mechanics
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Author : Jedrzej Sniatycki
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Geometric Quantization And Quantum Mechanics written by Jedrzej Sniatycki 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.
This book contains a revised and expanded version of the lecture notes of two seminar series given during the academic year 1976/77 at the Department of Mathematics and Statistics of the University of Calgary, and in the summer of 1978 at the Institute of Theoretical Physics of the Technical University Clausthal. The aim of the seminars was to present geometric quantization from the point of view· of its applica tions to quantum mechanics, and to introduce the quantum dynamics of various physical systems as the result of the geometric quantization of the classical dynamics of these systems. The group representation aspects of geometric quantiza tion as well as proofs of the existence and the uniqueness of the introduced structures can be found in the expository papers of Blattner, Kostant, Sternberg and Wolf, and also in the references quoted in these papers. The books of Souriau (1970) and Simms and Woodhouse (1976) present the theory of geometric quantization and its relationship to quantum mech anics. The purpose of the present book is to complement the preceding ones by including new developments of the theory and emphasizing the computations leading to results in quantum mechanics.
Lectures On The Geometry Of Quantization
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Author : Sean Bates
language : en
Publisher: American Mathematical Soc.
Release Date : 1997
Lectures On The Geometry Of Quantization written by Sean Bates 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 1997 with Mathematics categories.
These notes are based on a course entitled ``Symplectic Geometry and Geometric Quantization'' taught by Alan Weinstein at the University of California, Berkeley (fall 1992) and at the Centre Emile Borel (spring 1994). The only prerequisite for the course needed is a knowledge of the basic notions from the theory of differentiable manifolds (differential forms, vector fields, transversality, etc.). The aim is to give students an introduction to the ideas of microlocal analysis and the related symplectic geometry, with an emphasis on the role these ideas play in formalizing the transition between the mathematics of classical dynamics (hamiltonian flows on symplectic manifolds) and quantum mechanics (unitary flows on Hilbert spaces). These notes are meant to function as a guide to the literature. The authors refer to other sources for many details that are omitted and can be bypassed on a first reading.
Lectures On Geometric Quantization
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Author : D. J. Simms
language : en
Publisher:
Release Date : 2014-01-15
Lectures On Geometric Quantization written by D. J. Simms and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Hamiltonian Mechanical Systems And Geometric Quantization
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Author : Mircea Puta
language : en
Publisher: Springer
Release Date : 1993-06-30
Hamiltonian Mechanical Systems And Geometric Quantization written by Mircea Puta and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-06-30 with Mathematics categories.
The book is a revised and updated version of the lectures given by the author at the University of Timi§oara during the academic year 1990-1991. Its goal is to present in detail someold and new aspects ofthe geometry ofsymplectic and Poisson manifolds and to point out some of their applications in Hamiltonian mechanics and geometric quantization. The material is organized as follows. In Chapter 1 we collect some general facts about symplectic vector spaces, symplectic manifolds and symplectic reduction. Chapter 2 deals with the study ofHamiltonian mechanics. We present here the gen eral theory ofHamiltonian mechanicalsystems, the theory ofthe corresponding Pois son bracket and also some examples ofinfinite-dimensional Hamiltonian mechanical systems. Chapter 3 starts with some standard facts concerning the theory of Lie groups and Lie algebras and then continues with the theory ofmomentum mappings and the Marsden-Weinstein reduction. The theory of Hamilton-Poisson mechan ical systems makes the object of Chapter 4. Chapter 5 js dedicated to the study of the stability of the equilibrium solutions of the Hamiltonian and the Hamilton Poisson mechanical systems. We present here some of the remarcable results due to Holm, Marsden, Ra~iu and Weinstein. Next, Chapter 6 and 7 are devoted to the theory of geometric quantization where we try to solve, in a geometrical way, the so called Dirac problem from quantum mechanics. We follow here the construc tion given by Kostant and Souriau around 1964.
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 Quantization In Action
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Author : N.E. Hurt
language : en
Publisher: Springer Science & Business Media
Release Date : 1982-12-31
Geometric Quantization In Action written by N.E. Hurt 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 1982-12-31 with Mathematics categories.
Approach your problems from the right It isn't that they can't see the solution. It end and begin with the answers. Then, is that they can't see the problem. one day, perhaps you will fmd the final question. G. K. Chesterton, The Scandal of Father Brown 'The Point of a Pin'. 'The Hermit Clad in Crane Feathers' in R. Van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the 'tree' of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geo metry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical progmmming profit from homotopy theory; Lie algebras are relevant to fIltering; and prediction and electrical engineering can use Stein spaces.
The Geometry Of Heisenberg Groups
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Author : Ernst Binz
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
The Geometry Of Heisenberg Groups written by Ernst Binz 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 2008 with Mathematics categories.
"The three-dimensional Heisenberg group, being a quite simple non-commutative Lie group, appears prominently in various applications of mathematics. The goal of this book is to present basic geometric and algebraic properties of the Heisenberg group and its relation to other important mathematical structures (the skew field of quaternions, symplectic structures, and representations) and to describe some of its applications. In particular, the authors address such subjects as signal analysis and processing, geometric optics, and quantization. In each case, the authors present necessary details of the applied topic being considered." "This book manages to encompass a large variety of topics being easily accessible in its fundamentals. It can be useful to students and researchers working in mathematics and in applied mathematics."--BOOK JACKET.