[PDF] Representation Theory And Mathematical Physics eBook

Author : Anton Alekseev
Publisher : Springer Nature
Page : 652 pages
File Size : 42,97 MB
Release : 2022-02-05
Category : Mathematics
ISBN : 3030781488

GET BOOK

Over the course of his distinguished career, Nicolai Reshetikhin has made a number of groundbreaking contributions in several fields, including representation theory, integrable systems, and topology. The chapters in this volume – compiled on the occasion of his 60th birthday – are written by distinguished mathematicians and physicists and pay tribute to his many significant and lasting achievements. Covering the latest developments at the interface of noncommutative algebra, differential and algebraic geometry, and perspectives arising from physics, this volume explores topics such as the development of new and powerful knot invariants, new perspectives on enumerative geometry and string theory, and the introduction of cluster algebra and categorification techniques into a broad range of areas. Chapters will also cover novel applications of representation theory to random matrix theory, exactly solvable models in statistical mechanics, and integrable hierarchies. The recent progress in the mathematical and physicals aspects of deformation quantization and tensor categories is also addressed. Representation Theory, Mathematical Physics, and Integrable Systems will be of interest to a wide audience of mathematicians interested in these areas and the connections between them, ranging from graduate students to junior, mid-career, and senior researchers.

Author : Jialun Ping
Publisher : World Scientific Publishing Company
Page : 602 pages
File Size : 39,49 MB
Release : 2002-08-15
Category : Science
ISBN : 981310600X

GET BOOK

This book introduces systematically the eigenfunction method, a new approach to the group representation theory which was developed by the authors in the 1970's and 1980's in accordance with the concept and method used in quantum mechanics. It covers the applications of the group theory in various branches of physics and quantum chemistry, especially nuclear and molecular physics. Extensive tables and computational methods are presented.Group Representation Theory for Physicists may serve as a handbook for researchers doing group theory calculations. It is also a good reference book and textbook for undergraduate and graduate students who intend to use group theory in their future research careers.

Author : Peter Woit
Publisher : Springer
Page : 659 pages
File Size : 48,63 MB
Release : 2017-11-01
Category : Science
ISBN : 3319646125

GET BOOK

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 : Jürgen Fuchs
Publisher : American Mathematical Soc.
Page : 402 pages
File Size : 15,93 MB
Release : 2005
Category : Mathematics
ISBN : 0821837184

GET BOOK

Mathematics provides a language in which to formulate the laws that govern nature. It is a language proven to be both powerful and effective. In the quest for a deeper understanding of the fundamental laws of physics, one is led to theories that are increasingly difficult to put to the test. In recent years, many novel questions have emerged in mathematical physics, particularly in quantum field theory. Indeed, several areas of mathematics have lately become increasingly influentialin physics and, in turn, have become influenced by developments in physics. Over the last two decades, interactions between mathematicians and physicists have increased enormously and have resulted in a fruitful cross-fertilization of the two communities. This volume contains the plenary talks fromthe international symposium on Noncommutative Geometry and Representation Theory in Mathematical Physics held at Karlstad University (Sweden) as a satellite conference to the Fourth European Congress of Mathematics. The scope of the volume is large and its content is relevant to various scientific communities interested in noncommutative geometry and representation theory. It offers a comprehensive view of the state of affairs for these two branches of mathematical physics. The book is suitablefor graduate students and researchers interested in mathematical physics.

Author : Aleksandr Aleksandrovich Kirillov
Publisher : American Mathematical Soc.
Page : 247 pages
File Size : 31,29 MB
Release : 1991
Category : Mathematics
ISBN : 9780821841013

GET BOOK

Almost every major mathematical theory, from 19th century classical analysis and geometry to the newest abstract constructions of category theory, have recently acquired a ""physical flavour"". In the case of representation theory, two new areas of mathematical physics - the theory of completely integrable systems and string theory - have had a great influence. In addition, the idea of supersymmetry has become a general mathematical principle that has had important ramifications in representation theory. Together with this wave of new connections and new trends in representation theory, more traditional activity, dealing mostly with the study of classical objects, has also flourished. The papers in this volume were written by members of the seminar on representation theory at Moscow University, which has been running continuously since 1961. The papers reflect some of the new influences seen in representation theory today. Among the topics included are representation theory of ""large"" groups, indecomposable representations of the affine unimodular group of the plane, dual objects for certain real reductive Lie groups, and geometrical interpretations of a certain infinite-dimensional Lie algebra.

Author : Jeffrey Adams
Publisher : American Mathematical Soc.
Page : 404 pages
File Size : 35,11 MB
Release : 2011-11-07
Category : Mathematics
ISBN : 0821852469

GET BOOK

This volume contains the proceedings of the conference on Representation Theory and Mathematical Physics, in honor of Gregg Zuckerman's 60th birthday, held October 24-27, 2009, at Yale University. Lie groups and their representations play a fundamental role in mathematics, in particular because of connections to geometry, topology, number theory, physics, combinatorics, and many other areas. Representation theory is one of the cornerstones of the Langlands program in number theory, dating to the 1970s. Zuckerman's work on derived functors, the translation principle, and coherent continuation lie at the heart of the modern theory of representations of Lie groups. One of the major unsolved problems in representation theory is that of the unitary dual. The fact that there is, in principle, a finite algorithm for computing the unitary dual relies heavily on Zuckerman's work. In recent years there has been a fruitful interplay between mathematics and physics, in geometric representation theory, string theory, and other areas. New developments on chiral algebras, representation theory of affine Kac-Moody algebras, and the geometric Langlands correspondence are some of the focal points of this volume. Recent developments in the geometric Langlands program point to exciting connections between certain automorphic representations and dual fibrations in geometric mirror symmetry.

Author : A Barut
Publisher : World Scientific Publishing Company
Page : 740 pages
File Size : 32,40 MB
Release : 1986-11-01
Category : Mathematics
ISBN : 9813103876

GET BOOK

The material collected in this book originated from lectures given by authors over many years in Warsaw, Trieste, Schladming, Istanbul, Goteborg and Boulder. There is no other comparable book on group representations, neither in mathematical nor in physical literature and it is hoped that this book will prove to be useful in many areas of research. It is highly recommended as a textbook for an advanced course in mathematical physics on Lie algebras, Lie groups and their representations. Request Inspection Copy

Author : Robert S. Doran
Publisher : American Mathematical Soc.
Page : 460 pages
File Size : 44,66 MB
Release : 2008-01-17
Category : Mathematics
ISBN : 9780821857786

GET BOOK

George Mackey was an extraordinary mathematician of great power and vision. His profound contributions to representation theory, harmonic analysis, ergodic theory, and mathematical physics left a rich legacy for researchers that continues today. This book is based on lectures presented at an AMS special session held in January 2007 in New Orleans dedicated to his memory. The papers, written especially for this volume by internationally-known mathematicians and mathematical physicists, range from expository and historical surveys to original high-level research articles. The influence of Mackey's fundamental ideas is apparent throughout. The introductory article contains recollections from former students, friends, colleagues, and family as well as a biography describing his distinguished career as a mathematician at Harvard, where he held the Landon D. Clay Professorship of Mathematics. Topics examined here include recent results on induced representations, virtual groups, the Mackey Machine and crossed products, representations of Baumslag-Solitar groups, the Radon transform and the heat equation, groupoids in the study of wavelets, and quantum theory. The in-depth historical surveys of Mackey's work on representation theory, ergodic theory, and physics, together with recent developments inspired by his fundamental work will be of considerable interest to both graduate students and researchers alike.

Author : Alexander Varchenko
Publisher : World Scientific
Page : 383 pages
File Size : 46,69 MB
Release : 1995-03-29
Category : Mathematics
ISBN : 981450162X

GET BOOK

This book recounts the connections between multidimensional hypergeometric functions and representation theory. In 1984, physicists Knizhnik and Zamolodchikov discovered a fundamental differential equation describing correlation functions in conformal field theory. The equation is defined in terms of a Lie algebra. Kohno and Drinfeld found that the monodromy of the differential equation is described in terms of the quantum group associated with the Lie algebra. It turns out that this phenomenon is the tip of the iceberg. The Knizhnik-Zamolodchikov differential equation is solved in multidimensional hypergeometric functions, and the hypergeometric functions yield the connection between the representation theories of Lie algebras and quantum groups. The topics presented in this book are not adequately covered in periodicals.

Author : Jing-Song Huang
Publisher : Springer Science & Business Media
Page : 205 pages
File Size : 29,99 MB
Release : 2007-05-27
Category : Mathematics
ISBN : 0817644938

GET BOOK

This book presents a comprehensive treatment of important new ideas on Dirac operators and Dirac cohomology. Using Dirac operators as a unifying theme, the authors demonstrate how some of the most important results in representation theory fit together when viewed from this perspective. The book is an excellent contribution to the mathematical literature of representation theory, and this self-contained exposition offers a systematic examination and panoramic view of the subject. The material will be of interest to researchers and graduate students in representation theory, differential geometry, and physics.