  This article gives a review of the topic of regularising chiral gauge
theories and is aimed at a general audience. It begins by clarifying the
meaning of chirality and goes on to discussing chiral projections in field
theory, parity violation and the distinction between vector and chiral field
theories. It then discusses the standard model of electroweak interactions from
the perspective of chirality. It also reviews at length the phenomenon of
anomalies in quantum field theories including the intuitive understanding of
anomalies based on the Dirac sea picture as given by Nielsen and Ninomiya. It
then raises the issue of a non-perturbative and constructive definition of the
standard model as well as the importance of such formulations. The second
Nielsen-Ninomiya theorem about the impossibility of regularising chiral gauge
theories under some general assumptions is also discussed. After a brief review
of lattice regularisation of field theories, it discusses the issue of fermions
on the lattice with special emphasis on the problem of species doubling. The
implications of these problems to introducing chiral fermions on the lattice as
well as the interpretations of anomalies within the lattice formulations and
the lattice Dirac sea picture are then discussed. Finally the difficulties of
formulating the standard model on the lattice are illustrated through detailed
discussions of the Wilson-Yukawa method, the domain wall fermions method and
the recently popular Ginsparg-Wilson method.

High Energy Physics - Theory