  This work is devoted to incorporating into QFT the notion that particles and
hence the particle states should be localizable in space. It focuses on the
case of the Dirac field in 1+1 dimensional flat spacetime, generalizing a
recently developed formalism for scalar fields. This is achieved exploiting
again the non-uniqueness of quantization process. Instead of elementary
excitations carrying definite amounts of energy and momentum, we construct the
elementary excitations of the field localized (at some instant) in a definite
region of space. This construction not only leads to a natural notion of
localized quanta, but also provides a local algebra of operators. Once
constructed, the new representation is confronted to the standard global (Fock)
construction. In spite of being unitarily inequivalent representations, the
localized operators are well defined in the conventional Fock space. By using
them we dig up the issues of localization in QFT showing how the globality of
the vacuum state is responsible for the lack of a "common sense localization"
notion for particles in the standard Fock representation of QFT and propose a
method to meet its requirements.
