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 and power of the quantum deformation methods and
non-commutative geometry is illustrated on the different examples
starting from the simplest quantum mechanical system - harmonic
oscillator and ending with actual problems of modern field theory,
such as the attempts to construct lattice-like regularization
consistent with space-time Poincare symmetry and to incorporate
Higgs fields in the general geometrical frame of gauge theories.
Graduate students and researchers studying the problems of quantum
field theory, particle physics and mathematical aspects of quantum
symmetries will find the book of interest.
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