  We introduce a concise quantum operator formula for bosonization in which the
Lie group structure appears in a natural way. The connection between fermions
and bosons is found to be exactly the connection between Lie group elements and
the group parameters. Bosonization is an extraordinary way of expressing the
equation of motion of a complex fermion field in terms of a real scalar boson
in two dimensions. All the properties of the fermion field theory are known to
be preserved under this remarkable transformation with substantial
simplification and elucidation of the original theory, much like Lie groups can
be studied by their Lie algebras.

General Physics