  We generalize the concept of quasiparticle for one-dimensional (1D)
interacting electronic systems. The $\uparrow $ and $\downarrow $
quasiparticles recombine the pseudoparticle colors $c$ and $s$ (charge and spin
at zero magnetic field) and are constituted by one many-pseudoparticle {\it
topological momenton} and one or two pseudoparticles. These excitations cannot
be separated. We consider the case of the Hubbard chain. We show that the
low-energy electron -- quasiparticle transformation has a singular charater
which justifies the perturbative and non-perturbative nature of the quantum
problem in the pseudoparticle and electronic basis, respectively. This follows
from the absence of zero-energy electron -- quasiparticle overlap in 1D. The
existence of Fermi-surface quasiparticles both in 1D and three dimensional (3D)
many-electron systems suggests there existence in quantum liquids in dimensions
1$<$D$<$3. However, whether the electron -- quasiparticle overlap can vanish in
D$>$1 or whether it becomes finite as soon as we leave 1D remains an unsolved
question.
