Lectures On The Geometry Of Quantization
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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 : David John Simms
language : en
Publisher: Springer
Release Date : 1976
Lectures On Geometric Quantization written by David John Simms and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Science categories.
Lectures On Symplectic Manifolds
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Author : Alan Weinstein
language : en
Publisher: American Mathematical Soc.
Release Date : 1977
Lectures On Symplectic Manifolds written by Alan Weinstein 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 1977 with Mathematics categories.
The first six sections of these notes contain a description of some of the basic constructions and results on symplectic manifolds and lagrangian submanifolds. Section 7, on intersections of largrangian submanifolds, is still mostly internal to symplectic geometry, but it contains some applications to machanics and dynamical systems. Sections 8, 9, and 10 are devoted to various aspects of the quantization problem. In Section 10 there is a feedback of ideas from quantization theory into symplectic geometry itslef.
Lectures On The Geometry Of Poisson Manifolds
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Author : Izu Vaisman
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Lectures On The Geometry Of Poisson Manifolds written by Izu Vaisman and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This book is addressed to graduate students and researchers in the fields of mathematics and physics who are interested in mathematical and theoretical physics, differential geometry, mechanics, quantization theories and quantum physics, quantum groups etc., and who are familiar with differentiable and symplectic manifolds. The aim of the book is to provide the reader with a monograph that enables him to study systematically basic and advanced material on the recently developed theory of Poisson manifolds, and that also offers ready access to bibliographical references for the continuation of his study. Until now, most of this material was dispersed in research papers published in many journals and languages. The main subjects treated are the Schouten-Nijenhuis bracket; the generalized Frobenius theorem; the basics of Poisson manifolds; Poisson calculus and cohomology; quantization; Poisson morphisms and reduction; realizations of Poisson manifolds by symplectic manifolds and by symplectic groupoids and Poisson-Lie groups. The book unifies terminology and notation. It also reports on some original developments stemming from the author's work, including new results on Poisson cohomology and geometric quantization, cofoliations and biinvariant Poisson structures on Lie groups.
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.
Geometry And Quantization Of Moduli Spaces
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Author : Vladimir Fock
language : en
Publisher: Birkhäuser
Release Date : 2017-01-06
Geometry And Quantization Of Moduli Spaces written by Vladimir Fock and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-06 with Mathematics categories.
This volume is based on four advanced courses held at the Centre de Recerca Matemàtica (CRM), Barcelona. It presents both background information and recent developments on selected topics that are experiencing extraordinary growth within the broad research area of geometry and quantization of moduli spaces. The lectures focus on the geometry of moduli spaces which are mostly associated to compact Riemann surfaces, and are presented from both classical and quantum perspectives.
Geometry And Quantization
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Author :
language : en
Publisher:
Release Date : 2011
Geometry And Quantization written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Geometric quantization categories.
Quantization Geometry And Noncommutative Structures In Mathematics And Physics
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Author : Alexander Cardona
language : en
Publisher: Springer
Release Date : 2017-10-26
Quantization Geometry And Noncommutative Structures In Mathematics And Physics written by Alexander Cardona and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-26 with Science categories.
This monograph presents various ongoing approaches to the vast topic of quantization, which is the process of forming a quantum mechanical system starting from a classical one, and discusses their numerous fruitful interactions with mathematics.The opening chapter introduces the various forms of quantization and their interactions with each other and with mathematics.A first approach to quantization, called deformation quantization, consists of viewing the Planck constant as a small parameter. This approach provides a deformation of the structure of the algebra of classical observables rather than a radical change in the nature of the observables. When symmetries come into play, deformation quantization needs to be merged with group actions, which is presented in chapter 2, by Simone Gutt.The noncommutativity arising from quantization is the main concern of noncommutative geometry. Allowing for the presence of symmetries requires working with principal fiber bundles in a non-commutative setup, where Hopf algebras appear naturally. This is the topic of chapter 3, by Christian Kassel. Nichols algebras, a special type of Hopf algebras, are the subject of chapter 4, by Nicolás Andruskiewitsch. The purely algebraic approaches given in the previous chapters do not take the geometry of space-time into account. For this purpose a special treatment using a more geometric point of view is required. An approach to field quantization on curved space-time, with applications to cosmology, is presented in chapter 5 in an account of the lectures of Abhay Ashtekar that brings a complementary point of view to non-commutativity.An alternative quantization procedure is known under the name of string theory. In chapter 6 its supersymmetric version is presented. Superstrings have drawn the attention of many mathematicians, due to its various fruitful interactions with algebraic geometry, some of which are described here. The remaining chapters discuss further topics, as the Batalin-Vilkovisky formalism and direct products of spectral triples.This volume addresses both physicists and mathematicians and serves as an introduction to ongoing research in very active areas of mathematics and physics at the border line between geometry, topology, algebra and quantum field theory.
Quantization Pdes And Geometry
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Author : Dorothea Bahns
language : en
Publisher: Birkhäuser
Release Date : 2016-02-11
Quantization Pdes And Geometry written by Dorothea Bahns and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-11 with Mathematics categories.
This book presents four survey articles on different topics in mathematical analysis that are closely linked to concepts and applications in physics. Specifically, it discusses global aspects of elliptic PDEs, Berezin-Toeplitz quantization, the stability of solitary waves, and sub-Riemannian geometry. The contributions are based on lectures given by distinguished experts at a summer school in Göttingen. The authors explain fundamental concepts and ideas and present them clearly. Starting from basic notions, these course notes take the reader to the point of current research, highlighting new challenges and addressing unsolved problems at the interface between mathematics and physics. All contributions are of interest to researchers in the respective fields, but they are also accessible to graduate students.
Lectures On Non Perturbative Canonical Gravity
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Author : Abhay Ashtekar
language : en
Publisher: World Scientific
Release Date : 1991-07-03
Lectures On Non Perturbative Canonical Gravity written by Abhay Ashtekar and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-07-03 with Science categories.
Notes prepared in Collaboration with Ranjeet S Tate It is now generally recognized that perturbative field theoretical methods that have been highly successful in the quantum description of non-gravitational interactions cannot be used as a means of constructing a quantum theory of gravity. The primary aim of the book is to present an up- to-date account of a non-perturbative, canonical quantization program for gravity. Many of the technical results obtained in the process are of interest also to differential geometry, classical general relativity and QCD. The program as a whole was highlighted in virtually every major conference in gravitational physics over the past three years.