Mathematical Quantization - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Mathematical Quantization write by Nik Weaver. This book was released on 2001-05-31. Mathematical Quantization available in PDF, EPUB and Kindle. With a unique approach and presenting an array of new and intriguing topics, Mathematical Quantization offers a survey of operator algebras and related structures from the point of view that these objects are quantizations of classical mathematical structures. This approach makes possible, with minimal mathematical detail, a unified treatment of a
Geometric Quantization and Quantum Mechanics
Geometric Quantization and Quantum Mechanics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometric Quantization and Quantum Mechanics write by Jedrzej Sniatycki. This book was released on 2012-12-06. Geometric Quantization and Quantum Mechanics available in PDF, EPUB and Kindle. 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.
Quantization, Geometry and Noncommutative Structures in Mathematics and Physics
Quantization, Geometry and Noncommutative Structures in Mathematics and Physics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Quantization, Geometry and Noncommutative Structures in Mathematics and Physics write by Alexander Cardona. This book was released on 2017-10-26. Quantization, Geometry and Noncommutative Structures in Mathematics and Physics available in PDF, EPUB and Kindle. 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.
Geometric Quantization
Geometric Quantization - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometric Quantization write by Nicholas Michael John Woodhouse. This book was released on 1992. Geometric Quantization available in PDF, EPUB and Kindle. The geometric approach to quantization was introduced by Konstant and Souriau more than 20 years ago. It has given valuable and lasting insights into the relationship between classical and quantum systems, and continues to be a popular research topic. The ideas have proved useful in pure mathematics, notably in representation theory, as well as in theoretical physics. The most recent applications have been in conformal field theory and in the Jones-Witten theory of knots. The successful original edition of this book was published in 1980. Now it has been completely revised and extensively rewritten. The presentation has been simplified and many new examples have been added. The material on field theory has been expanded.
Mathematical Aspects Of Weyl Quantization And Phase
Mathematical Aspects Of Weyl Quantization And Phase - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Mathematical Aspects Of Weyl Quantization And Phase write by Daniel Abrom Dubin. This book was released on 2000-06-12. Mathematical Aspects Of Weyl Quantization And Phase available in PDF, EPUB and Kindle. This book analyzes in considerable generality the quantization-dequantization integral transform scheme of Weyl and Wigner, and considers several phase operator theories. It features: a thorough treatment of quantization in polar coordinates; dequantization by a new method of “motes”; a discussion of Moyal algebras; modifications of the transform method to accommodate operator orderings; a rigorous discussion of the Dicke laser model for one mode, fully quantum, in the thermodynamic limit; analysis of quantum phase theories based on the Toeplitz operator, the coherent state operator, the quantized phase space angle, and a sequence of finite rank operators.
