Quantum Groups, Quantum Categories and Quantum Field Theory
Quantum Groups, Quantum Categories and Quantum Field Theory

Author: Jürg Fröhlich

Publisher: Springer

Published: 2006-11-15

Total Pages: 438

ISBN-13: 3540476113

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This book reviews recent results on low-dimensional quantum field theories and their connection with quantum group theory and the theory of braided, balanced tensor categories. It presents detailed, mathematically precise introductions to these subjects and then continues with new results. Among the main results are a detailed analysis of the representation theory of U (sl ), for q a primitive root of unity, and a semi-simple quotient thereof, a classfication of braided tensor categories generated by an object of q-dimension less than two, and an application of these results to the theory of sectors in algebraic quantum field theory. This clarifies the notion of "quantized symmetries" in quantum fieldtheory. The reader is expected to be familiar with basic notions and resultsin algebra. The book is intended for research mathematicians, mathematical physicists and graduate students.

Quantum Groups
Quantum Groups

Author: Christian Kassel

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 540

ISBN-13: 1461207835

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Here is an introduction to the theory of quantum groups with emphasis on the spectacular connections with knot theory and Drinfeld's recent fundamental contributions. It presents the quantum groups attached to SL2 as well as the basic concepts of the theory of Hopf algebras. Coverage also focuses on Hopf algebras that produce solutions of the Yang-Baxter equation and provides an account of Drinfeld's elegant treatment of the monodromy of the Knizhnik-Zamolodchikov equations.

Quantum Theory, Groups and Representations
Quantum Theory, Groups and Representations

Author: Peter Woit

Publisher: Springer

Published: 2017-11-01

Total Pages: 659

ISBN-13: 3319646125

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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.

Foundations of Quantum Group Theory
Foundations of Quantum Group Theory

Author: Shahn Majid

Publisher: Cambridge University Press

Published: 2000

Total Pages: 668

ISBN-13: 9780521648684

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A graduate level text which systematically lays out the foundations of Quantum Groups.

Introduction to Quantum Groups
Introduction to Quantum Groups

Author: George Lusztig

Publisher: Springer Science & Business Media

Published: 2010-10-27

Total Pages: 361

ISBN-13: 0817647171

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The quantum groups discussed in this book are the quantized enveloping algebras introduced by Drinfeld and Jimbo in 1985, or variations thereof. The theory of quantum groups has led to a new, extremely rigid structure, in which the objects of the theory are provided with canonical basis with rather remarkable properties. This book will be of interest to mathematicians working in the representation theory of Lie groups and Lie algebras, knot theorists and to theoretical physicists and graduate students. Since large parts of the book are independent of the theory of perverse sheaves, the book could also be used as a text book.

Affine Lie Algebras and Quantum Groups
Affine Lie Algebras and Quantum Groups

Author: Jürgen Fuchs

Publisher: Cambridge University Press

Published: 1995-03-09

Total Pages: 452

ISBN-13: 9780521484121

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This is an introduction to the theory of affine Lie Algebras, to the theory of quantum groups, and to the interrelationships between these two fields that are encountered in conformal field theory.

Quantum Groups in Two-Dimensional Physics
Quantum Groups in Two-Dimensional Physics

Author: Cisar Gómez

Publisher: Cambridge University Press

Published: 1996-04-18

Total Pages: 477

ISBN-13: 0521460654

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A 1996 introduction to integrability and conformal field theory in two dimensions using quantum groups.

From Field Theory to Quantum Groups
From Field Theory to Quantum Groups

Author: Bernard Jancewicz

Publisher: World Scientific

Published: 1996

Total Pages: 351

ISBN-13: 981022544X

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Professor Jerzy Lukierski, an outstanding specialist in the domain of quantum groups, will reach on May 21, 1995 the age of sixty. This is a birthday volume dedicated to him. It assumes the form of a collection of papers on a wide range of topics in modern research area from theoretical high energy physics to mathematical physics. Various topics of quantum groups will be treated with a special emphasis. Quantum groups is nowadays a very fashionable subject both in mathematics and high energy physics.

Lectures on Algebraic Quantum Groups
Lectures on Algebraic Quantum Groups

Author: Ken Brown

Publisher: Birkhäuser

Published: 2012-12-06

Total Pages: 339

ISBN-13: 303488205X

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This book consists of an expanded set of lectures on algebraic aspects of quantum groups. It particularly concentrates on quantized coordinate rings of algebraic groups and spaces and on quantized enveloping algebras of semisimple Lie algebras. Large parts of the material are developed in full textbook style, featuring many examples and numerous exercises; other portions are discussed with sketches of proofs, while still other material is quoted without proof.

Group Theory and Quantum Mechanics
Group Theory and Quantum Mechanics

Author: Michael Tinkham

Publisher: Courier Corporation

Published: 2012-04-20

Total Pages: 354

ISBN-13: 0486131661

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This graduate-level text develops the aspects of group theory most relevant to physics and chemistry (such as the theory of representations) and illustrates their applications to quantum mechanics. The first five chapters focus chiefly on the introduction of methods, illustrated by physical examples, and the final three chapters offer a systematic treatment of the quantum theory of atoms, molecules, and solids. The formal theory of finite groups and their representation is developed in Chapters 1 through 4 and illustrated by examples from the crystallographic point groups basic to solid-state and molecular theory. Chapter 5 is devoted to the theory of systems with full rotational symmetry, Chapter 6 to the systematic presentation of atomic structure, and Chapter 7 to molecular quantum mechanics. Chapter 8, which deals with solid-state physics, treats electronic energy band theory and magnetic crystal symmetry. A compact and worthwhile compilation of the scattered material on standard methods, this volume presumes a basic understanding of quantum theory.