Quantized Algebra And Physics
DOWNLOAD
Download Quantized Algebra And Physics PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Quantized Algebra And Physics book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Quantized Algebra And Physics
DOWNLOAD
Author : Chengming Bai
language : en
Publisher: World Scientific
Release Date : 2012
Quantized Algebra And Physics written by Chengming Bai and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
A note on Brauer-Schur functions / Kazuya Aokage, Hiroshi Mizukawa and Hiro-Fumi Yamada -- [symbol]-operators on associative algebras, associative Yang-Baxter equations and dendriform algebras / Chengming Bai, Li Guo and Xiang Ni -- Irreducible Wakimoto-like modules for the affine Lie algebra [symbol] / Yun Gao and Ziting Zeng -- Verma modules over generic exp-polynomial Lie algebras / Xiangqian Guo, Xuewen Liu and Kaiming Zhao -- A formal infinite dimensional Cauchy problem and its relation to integrable hierarchies / G.F. Helminck, E.A. Panasenko and A.O. Sergeeva -- Partially harmonic tensors and quantized Schur-Weyl duality / Jun Hu and Zhankui Xiao -- Quantum entanglement and approximation by positive matrices / Xiaofen Huang and Naihuan Jing -- 2-partitions of root systems / Bin Li, William Wong and Hechun Zhang -- A survey on weak Hopf algebras / Fang Li and Qinxiu Sun -- The equitable presentation for the quantum algebra Uq(f(k)) / Yan Pan, Meiling Zhu and Libin Li
Quantization Geometry And Noncommutative Structures In Mathematics And Physics
DOWNLOAD
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.
Quantum Groups And Their Representations
DOWNLOAD
Author : Anatoli Klimyk
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Quantum Groups And Their Representations written by Anatoli Klimyk 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 start with an introduction to quantum groups for the beginner and continues as a textbook for graduate students in physics and in mathematics. It can also be used as a reference by more advanced readers. The authors cover a large but well-chosen variety of subjects from the theory of quantum groups (quantized universal enveloping algebras, quantized algebras of functions) and q-deformed algebras (q-oscillator algebras), their representations and corepresentations, and noncommutative differential calculus. The book is written with potential applications in physics and mathematics in mind. The basic quantum groups and quantum algebras and their representations are given in detail and accompanied by explicit formulas. A number of topics and results from the more advanced general theory are developed and discussed.
Mathematical Quantization
DOWNLOAD
Author : Nik Weaver
language : en
Publisher: CRC Press
Release Date : 2001-05-31
Mathematical Quantization written by Nik Weaver and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-05-31 with Mathematics categories.
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
Deformation Theory And Quantum Groups With Applications To Mathematical Physics
DOWNLOAD
Author : Murray Gerstenhaber
language : en
Publisher: American Mathematical Soc.
Release Date : 1992-01-01
Deformation Theory And Quantum Groups With Applications To Mathematical Physics written by Murray Gerstenhaber 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 1992-01-01 with Mathematics categories.
Quantum groups are not groups at all, but special kinds of Hopf algebras of which the most important are closely related to Lie groups and play a central role in the statistical and wave mechanics of Baxter and Yang. Those occurring physically can be studied as essentially algebraic and closely related to the deformation theory of algebras (commutative, Lie, Hopf, and so on). One of the oldest forms of algebraic quantization amounts to the study of deformations of a commutative algebra A (of classical observables) to a noncommutative algebra A*h (of operators) with the infinitesimal deformation given by a Poisson bracket on the original algebra A. This volume grew out of an AMS--IMS--SIAM Joint Summer Research Conference, held in June 1990 at the University of Massachusetts at Amherst. The conference brought together leading researchers in the several areas mentioned and in areas such as ''q special functions'', which have their origins in the last century but whose relevance to modern physics has only recently been understood. Among the advances taking place during the conference was Majid's reconstruction theorem for Drinfel$'$d's quasi-Hopf algebras. Readers will appreciate this snapshot of some of the latest developments in the mathematics of quantum groups and deformation theory.
Mathematics Of Quantization And Quantum Fields
DOWNLOAD
Author : Jan Dereziński
language : en
Publisher: Cambridge University Press
Release Date : 2013-03-07
Mathematics Of Quantization And Quantum Fields written by Jan Dereziński and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-07 with Science categories.
A unique and definitive review of mathematical aspects of quantization and quantum field theory for graduate students and researchers.
Quantization Poisson Brackets And Beyond
DOWNLOAD
Author : Theodore Voronov
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Quantization Poisson Brackets And Beyond written by Theodore Voronov 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 2002 with Geometric quantization categories.
The papers in this volume are based on talks given at the 2001 Manchester Meeting of the London Mathematical Society, which was followed by an international workshop on Quantization, Deformations, and New Homological and Categorical Methods in Mathematical Physics. Focus is on the topics suggested by the title: quantization in its various aspects, Poisson brackets and generalizations, and structures beyond'' this, including symplectic supermanifolds, operads, Lie groupoids and Lie (bi)algebroids, and algebras with $n$-ary operations. The book offers accounts of up-to-date results as well as accessible expositions aimed at a broad reading audience of researchers in differential geometry, algebraic topology and mathematical physics.
Algebras Of Functions On Quantum Groups Part I
DOWNLOAD
Author : Leonid I. Korogodski
language : en
Publisher: American Mathematical Soc.
Release Date : 1998
Algebras Of Functions On Quantum Groups Part I written by Leonid I. Korogodski 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 1998 with Function algebras categories.
The text is devoted to the study of algebras of functions on quantum groups. The book includes the theory of Poisson-Lie algebras (quasi-classical version of algebras of functions on quantum groups), a description of representations of algebras of functions and the theory of quantum Weyl groups. It can serve as a text for an introduction to the theory of quantum groups and is intended for graduate students and research mathematicians working in algebra, representation theory and mathematical physics.
Integrability Quantization And Geometry I Integrable Systems
DOWNLOAD
Author : Sergey Novikov
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-04-12
Integrability Quantization And Geometry I Integrable Systems written by Sergey Novikov 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 2021-04-12 with Education categories.
This book is a collection of articles written in memory of Boris Dubrovin (1950–2019). The authors express their admiration for his remarkable personality and for the contributions he made to mathematical physics. For many of the authors, Dubrovin was a friend, colleague, inspiring mentor, and teacher. The contributions to this collection of papers are split into two parts: “Integrable Systems” and “Quantum Theories and Algebraic Geometry”, reflecting the areas of main scientific interests of Dubrovin. Chronologically, these interests may be divided into several parts: integrable systems, integrable systems of hydrodynamic type, WDVV equations (Frobenius manifolds), isomonodromy equations (flat connections), and quantum cohomology. The articles included in the first part are more or less directly devoted to these areas (primarily with the first three listed above). The second part contains articles on quantum theories and algebraic geometry and is less directly connected with Dubrovin's early interests.
Deformation Quantization For Actions Of R D
DOWNLOAD
Author : Marc Aristide Rieffel
language : en
Publisher: American Mathematical Soc.
Release Date : 1993
Deformation Quantization For Actions Of R D written by Marc Aristide Rieffel 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 1993 with Mathematics categories.
This work describes a general construction of a deformation quantization for any Poisson bracket on a manifold which comes from an action of $R^d$ on that manifold. These deformation quantizations are strict, in the sense that the deformed product of any two functions is again a function and that there are corresponding involutions and operator norms. Many of the techniques involved are adapted from the theory of pseudo-differential operators. The construction is shown to have many favorable properties. A number of specific examples are described, ranging from basic ones such as quantum disks, quantum tori, and quantum spheres, to aspects of quantum groups.