  We find the singular transformation between the electron operator and the
pseudoparticle operators for the Hubbard chain. We generalize the concept of
quasiparticle to one-dimensional electronic systems which in 1D refers to
many-pseudoparticle objects. We obtain explicit results for the electron
renormalization factor, self energy, and vertex functions at the Fermi points.
We also discuss the possible connection of our results to higher dimensions and
explore the possibilities of instabilities in the interacting problem such as
the formation of Cooper pairs.
