This is a monograph on geometrical and topological features which
arise in quantum field theory. It is well known that when a chiral
fermion interacts with a gauge field we have chiral anomaly which
corresponds to the fact that divergence of the axial vector current
does not vanish. It is observed that this is related to certain
topological features associated with the fermion and leads to the
realization of the topological origin of fermion number as well as
the Berry phase. The role of gauge fields in the quantization
procedure has its implications in these topological features of a
fermion and helps us to consider a massive fermion as a soliton
(skyrrnion). In this formalism chiral anomaly is found to be
responsible for mass generation. This has its relevance in
electroweak theory where it is observed that weak interaction gauge
bosons attain mass topologically. The geometrical feature of a
skyrmion also helps us to realize the internal symmetry of hadrons
from reflection group. Finally it has been shown that
noncommutative geometry where the space time manifold is taken to
be X = M x Zz has its relevance in the description of a massive 4
fermion as a skyrmion when the discrete space is considered as the
internal space and the symmetry breaking leads to chiral anomaly.
In chap. l preliminary mathematical formulations related to the
spinor structure have been discussed. In chap.
General
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