Introduction to quantum groups / M. Chaichian, A. Demichev.

Format:

Book

Author/Creator:

Chaichian, M. (Masud), 1941-

Contributor:

Demichev, A. P. (Andrei Pavlovich)

Language:

English

Subjects (All):

Quantum groups.

Physical Description:

1 online resource (357 p.)

Other Title:

Quantum groups

Place of Publication:

Singapore ; River Edge, N.J. : World Scientific, c1996.

Language Note:

English

Summary:

In the past decade there has been an extemely rapid growth in the interest and development of quantum group theory.This book provides students and researchers with a practical introduction to the principal ideas of quantum groups theory and its applications to quantum mechanical and modern field theory problems. It begins with a review of, and introduction to, the mathematical aspects of quantum deformation of classical groups, Lie algebras and related objects (algebras of functions on spaces, differential and integral calculi). In the subsequent chapters the richness of mathematical structure

Contents:

Preface; Contents; Introduction; Notational Conventions; Chapter 1 Mathematical Aspects of Quantum Group Theory and Non-Commutative Geometry; 1.1 Non-commutative algebras differential calculi transformations and all that; 1.2 Hopf algebra and Poisson structure of classical Lie groups and algebras; 1.3 Deformation of co-Poisson structures; 1.4 Quasi-triangular Hopf algebras and quantum double construction; 1.5 Quantum matrix groups; 1.5.1 Quantum groups GLq(n) and SLq(n); 1.5.2 Quantum groups SOq(N) and Spq(n); 1.5.3 Twists of quantum groups and multiparametric deformations

1.6 Quantum deformation of differential and integral calculi1.6.1 Differential calculus on q-groups; 1.6.2 Differential calculus on quantum spaces; 1.6.3 q-Deformation of integral calculus; 1.7 Elements of quantum group representations; 1.7.1 Corepresentations of quantum groups; 1.7.2 Representations of quantum universal enveloping algebras; 1.7.3 Representations of quantized algebras of functions; Chapter 2 q-Deformation of Harmonic Oscillators Quantum Symmetry and All That; 2.1 q-Deformation of single harmonic oscillator

2.2 Bargmann-Fock representation for q-oscillator algebra in terms of operators on quantum planes2.3 Quasi-classical limit of q-oscillators and q-deformed path integrals; 2.3.1 Quasi-classical limit of q-oscillators (with real parameter of deformation); 2.3.2 Path integral for q-oscillators (real q); 2.3.3 Path integral for q-oscillators with root of unity value of deformation parameter; 2.4 q-Oscillators and representations of QUEA; 2.4.1 q-Deformed Jordan-Schwinger realization; 2.4.2 Quantum Clebsch-Gordan coefficients and Wigner-Eckart theorem; 2.4.3 Covariant systems of q-oscillators

2.5 q-Deformation of supergroups and conception of braided groups2.5.1 q-Supergroups q-superalgebras and q-superoscillators; 2.5.2 Braided groups and spaces; 2.6 Quantum symmetries and q-deformed algebras in physical systems; 2.6.1 Integrable one-dimensional spin-chain model; 2.6.2 A model in quantum optics; 2.6.3 Magnetic translations and the algebra slq(2); 2.6.4 Pseudoeuclidian quantum algebra as symmetry of phonons; 2.6.5 q-Oscillators and regularization of quantum field theory; 2.6.6 q-Deformed statistics and the ideal q-gas

2.6.7 Nonlinear Regge trajectory and quantum dual string theory2.6.8 q-Deformation of the Virasoro algebra; Chapter 3 q-Deformation of Space-Time Symmetries; 3.1 One-dimensional lattice and q-deformation of differential calculus; 3.2 Multidimensional Jackson calculus and particle on two-dimensional quantum space; 3.3 Projective construction of quantum inhomogeneous groups; 3.4 Twisted Poincare group and geometry of q-deformed Minkowski space; 3.4.1 Quantum deformation of the Poincare group; 3.4.2 Quantum Minkowski geometry; 3.4.3 q-tetrades and transformation to commuting coordinates

3.4.4 Twisted Poincare algebra and induced representations of the q-group

Notes:

Description based upon print version of record.

Includes bibliographical references (p. 323-337) and index.

ISBN:

9789814261067

9814261068