The quantum Hall effect (QHE) is one of the most fascinating and
beautiful phenomena in all branches of physics. Tremendous
theoretical and experimental developments are still being made in
this sphere. In the original edition of this book, composite
bosons, composite fermions and fractional charged excitations
(anyons) were among the distinguished ideas presented. This new
edition includes many novel ideas according to recent progress.
Fantastic phenomena associated with the interlayer phase coherence
and SU(4) quantum Hall ferromagnets in the bilayer system are
extensively reviewed. The microscopic theory of the QHE is
formulated based on noncommutative geometry, the underlying
mathematical structure. Quasiparticles are described as
noncommutative solitons. The coverage also includes the recent
development of the unconventional QHE in graphene (a single atomic
layer graphite), where the electron dynamics can be treated as
relativistic Dirac fermions and even the supersymmetric quantum
mechanics plays a key role. An instructive and comprehensive
overview of the QHE, the book is also suitable as an introduction
to quantum field theory with vivid applications. Only a knowledge
of quantum mechanics is assumed.
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