This book aims to describe the physics of the integer and
fractional quantum Hall effects (QHE) from a theoretical side. In
the classical Hall effect, the Hall resistance is proportional to
the applied magnetic field strength and varies continuously. So,
the discovery of a stepwise change of the Hall resistance by von
Klitzing in an ultra-thin layer of a MOSFET was a big surprise. The
QHE is a macroscopic phenomenon and shows the exact quantum
structure, which is one of the most fundamental phenomena in
physics. The fractional quantum Hall effect has been explained
assuming quasi-particles with fractional charges or Jain's
composite fermions, the existence of which has not been verified
experimentally. The author has been developing a theory based on a
standard treatment of an interacting electron system without
assuming any quasi-particle. This book will be easily understood by
undergraduate students in physics. Knowledge of quantum field
theory is needed to study Chapter 9.
General
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