Lie Groups Quantization Volume 1
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| Author | : Veronique Fischer |
| Publisher | : Birkhäuser |
| Total Pages | : 568 |
| Release | : 2016-03-08 |
| Genre | : Mathematics |
| ISBN | : 3319295586 |
This book presents a consistent development of the Kohn-Nirenberg type global quantization theory in the setting of graded nilpotent Lie groups in terms of their representations. It contains a detailed exposition of related background topics on homogeneous Lie groups, nilpotent Lie groups, and the analysis of Rockland operators on graded Lie groups together with their associated Sobolev spaces. For the specific example of the Heisenberg group the theory is illustrated in detail. In addition, the book features a brief account of the corresponding quantization theory in the setting of compact Lie groups. The monograph is the winner of the 2014 Ferran Sunyer i Balaguer Prize.
| Author | : Peter Woit |
| Publisher | : Springer |
| Total Pages | : 659 |
| Release | : 2017-11-01 |
| Genre | : Science |
| ISBN | : 3319646125 |
This text systematically presents the basics of quantum mechanics, emphasizing the role of Lie groups, Lie algebras, and their unitary representations. The mathematical structure of the subject is brought to the fore, intentionally avoiding significant overlap with material from standard physics courses in quantum mechanics and quantum field theory. The level of presentation is attractive to mathematics students looking to learn about both quantum mechanics and representation theory, while also appealing to physics students who would like to know more about the mathematics underlying the subject. This text showcases the numerous differences between typical mathematical and physical treatments of the subject. The latter portions of the book focus on central mathematical objects that occur in the Standard Model of particle physics, underlining the deep and intimate connections between mathematics and the physical world. While an elementary physics course of some kind would be helpful to the reader, no specific background in physics is assumed, making this book accessible to students with a grounding in multivariable calculus and linear algebra. Many exercises are provided to develop the reader's understanding of and facility in quantum-theoretical concepts and calculations.
| Author | : Molin Ge |
| Publisher | : World Scientific Publishing Company |
| Total Pages | : 596 |
| Release | : 2016-02-16 |
| Genre | : Science |
| ISBN | : 9814340960 |
This unique volume summarizes with a historical perspective several of the major scientific achievements of Ludwig Faddeev, with a foreword by Nobel Laureate C N Yang. The volume that spans over fifty years of Faddeev's career begins where he started his own scientific research, in the subject of scattering theory and the three-body problem. It then continues to describe Faddeev's contributions to automorphic functions, followed by an extensive account of his many fundamental contributions to quantum field theory including his original article on ghosts with Popov. Faddeev's contributions to soliton theory and integrable models are then described, followed by a survey of his work on quantum groups. The final scientific section is devoted to Faddeev's contemporary research including articles on his long-term interest in constructing knotted solitons and understanding confinement. The volume concludes with his personal view on science and mathematical physics in particular.
| Author | : Leonid I. Korogodski |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 162 |
| Release | : 1998 |
| Genre | : Mathematics |
| ISBN | : 0821803360 |
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.
| Author | : Garth Warner |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 545 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 364250275X |
The representation theory of locally compact groups has been vig orously developed in the past twenty-five years or so; of the various branches of this theory, one of the most attractive (and formidable) is the representation theory of semi-simple Lie groups which, to a great extent, is the creation of a single man: Harish-Chandra. The chief objective of the present volume and its immediate successor is to provide a reasonably self-contained introduction to Harish-Chandra's theory. Granting cer tain basic prerequisites (cf. infra), we have made an effort to give full details and complete proofs of the theorems on which the theory rests. The structure of this volume and its successor is as follows. Each book is divided into chapters; each chapter is divided into sections; each section into numbers. We then use the decimal system of reference; for example, 1. 3. 2 refers to the second number in the third section of the first chapter. Theorems, Propositions, Lemmas, and Corollaries are listed consecutively throughout any given number. Numbers which are set in fine print may be omitted at a first reading. There are a variety of Exam ples scattered throughout the text; the reader, if he is so inclined, can view them as exercises ad libitum. The Appendices to the text collect certain ancillary results which will be used on and off in the systematic exposi tion; a reference of the form A2.
| Author | : Roger William Carter |
| Publisher | : Cambridge University Press |
| Total Pages | : 662 |
| Release | : 2005-10-27 |
| Genre | : Mathematics |
| ISBN | : 9780521851381 |
This book provides a thorough but relaxed mathematical treatment of Lie algebras.
| Author | : J. Bertrand |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 329 |
| Release | : 2013-06-29 |
| Genre | : Science |
| ISBN | : 9401585431 |
This book contains the proceedings of a meeting that brought together friends and colleagues of Guy Rideau at the Université Denis Diderot (Paris, France) in January 1995. It contains original results as well as review papers covering important domains of mathematical physics, such as modern statistical mechanics, field theory, and quantum groups. The emphasis is on geometrical approaches. Several papers are devoted to the study of symmetry groups, including applications to nonlinear differential equations, and deformation of structures, in particular deformation-quantization and quantum groups. The richness of the field of mathematical physics is demonstrated with topics ranging from pure mathematics to up-to-date applications such as imaging and neuronal models. Audience: Researchers in mathematical physics.
| Author | : Vyjayanthi Chari |
| Publisher | : Cambridge University Press |
| Total Pages | : 672 |
| Release | : 1995-07-27 |
| Genre | : Mathematics |
| ISBN | : 9780521558846 |
Since they first arose in the 1970s and early 1980s, quantum groups have proved to be of great interest to mathematicians and theoretical physicists. The theory of quantum groups is now well established as a fascinating chapter of representation theory, and has thrown new light on many different topics, notably low-dimensional topology and conformal field theory. The goal of this book is to give a comprehensive view of quantum groups and their applications. The authors build on a self-contained account of the foundations of the subject and go on to treat the more advanced aspects concisely and with detailed references to the literature. Thus this book can serve both as an introduction for the newcomer, and as a guide for the more experienced reader. All who have an interest in the subject will welcome this unique treatment of quantum groups.
| Author | : Kevin Costello |
| Publisher | : Cambridge University Press |
| Total Pages | : 399 |
| Release | : 2017 |
| Genre | : Mathematics |
| ISBN | : 1107163102 |
This first volume develops factorization algebras with a focus upon examples exhibiting their use in field theory, which will be useful for researchers and graduates.
| Author | : Marián Fecko |
| Publisher | : Cambridge University Press |
| Total Pages | : 11 |
| Release | : 2006-10-12 |
| Genre | : Science |
| ISBN | : 1139458035 |
Covering subjects including manifolds, tensor fields, spinors, and differential forms, this textbook introduces geometrical topics useful in modern theoretical physics and mathematics. It develops understanding through over 1000 short exercises, and is suitable for advanced undergraduate or graduate courses in physics, mathematics and engineering.
