Tremendous theoretical and experimental developments have recently been made in the sphere of the quantum Hall effect. Among them a field-theoretical approach has presented a fascinating unified physical picture. A most significant feature of the quantum Hall system is that exotic phenomena associated with statistics transmutation are realized. For instance, an electron may undergo Bose condensation by making a charge-flux composite, and fractionally charged excitations (anyons) emerge as quasiparticles. A pedagogical and self-contained discussion on monolayer and bilayer quantum Hall systems is given in a field-theoretical framework, together with an introduction to quantum field theory, anyon physics and Chern–Simons gauge theory. Only knowledge of quantum mechanics is assumed.

This invaluable book will be of great interest to students and researchers in condensed-matter, theoretical, particle and mathematical physics.

Contents:

• Quantum Field Theory:
• Quantum Mechanics
• Quantum Field Theory
• Canonical Quantization
• Spontaneous Symmetry Breaking
• Electromagnetic Field
• Topological Solitons
• Anyons
• Monolayer Quantum Hall Systems:
• Landau Quantization
• Quantum Hall Effects
• Quasiparticles and Activation Energy
• Field Theory of Composite Particles
• Composite Bosons and Semiclassical Analysis
• Quantum Hall Ferromagnets
• Spin Textures
• Hierarchy of Fractional Quantum Hall States
• Edge Effects
• Bilayer Quantum Hall Systems:
• SU(2) Pseudospin Structure
• Bilayer-Locked States
• Interlayer-Coherent States
• Skyrmions in SU(4)-Invariant Regime
• Bilayer Quantum-Hall Junction
• Algebraic Approach:
• Lowest-Landau-Level Projection
• Quantum Hall Effects in Algebraic Approach
• Effective Hamiltonian in Algebraic Approach
• Electric Currents in Bilayer Systems

"The book is extremely well written, and it is a most readable book on the topic for particle-field physicists ... For instance, the description of the Electromagnetic Field in Chapter 5 is very lucid as it provides a natural bridge between the Higgs model and superconductivity in simple terms."

"Professor Ezawa has written an extremely useful book on the theory of the Quantum Hall Effect. The book covers a wide range, starting from the spectacular discoveries of the Hall conductivity plateaus all the way to the most recent developments in double-layer systems ... The book is also very attractively produced with numerous graphs and colorful figures to illustrate the ideas."

"This book gives an excellent account of these developments. The presentation of the extensive material is masterful ... it is recommended for an advanced graduate student learning about new many-body techniques beyond the ones taught in courses based on the Green functions, etc."

"This is a textbook which is very well organized and carefully written from a unique point of view. I recommend this book not only to condensed matter physicists but also to elementary particle theorists as an excellent example of the successful application of the field theory to condensed matter physics. This book will also be an excellent introduction to study field theory."