This book introduces aspects of topology and applications to problems in
condensed matter physics. Basic topics in mathematics have been
introduced in a form accessible to physicists, and the use of topology
in quantum, statistical and solid state physics has been developed with
an emphasis on pedagogy. The aim is to bridge the language barrier
between physics and mathematics, as well as the different
specializations in physics. Pitched at the level of a graduate student
of physics, this book does not assume any additional knowledge of
mathematics or physics. It is therefore suited for advanced postgraduate
students as well. A collection of selected problems will help the reader
learn the topics on one's own, and the broad range of topics covered
will make the text a valuable resource for practising researchers in the
field.
The book consists of two parts: one corresponds to developing the
necessary mathematics and the other discusses applications to physical
problems. The section on mathematics is a quick, but more-or-less
complete, review of topology. The focus is on explaining fundamental
concepts rather than dwelling on details of proofs while retaining the
mathematical flavour. There is an overview chapter at the beginning and
a recapitulation chapter on group theory. The physics section starts
with an introduction and then goes on to topics in quantum mechanics,
statistical mechanics of polymers, knots, and vertex models, solid state
physics, exotic excitations such as Dirac quasiparticles, Majorana
modes, Abelian and non-Abelian anyons. Quantum spin liquids and quantum
information-processing are also covered in some detail.
