  Standard bosonization techniques lead to phonon-like excitations in a
Luttinger liquid (LL), reflecting the absence of Landau quasiparticles in these
systems. Yet in addition to the above excitations some LL are known to possess
solitonic states carrying fractional quantum numbers (e.g. the spin 1/2
Heisenberg chain). We have reconsidered the zero modes in the low-energy
spectrum of the gaussian boson LL hamiltonian both for fermionic and bosonic
LL: in the spinless case we find that two elementary excitations carrying
fractional quantum numbers allow to generate all the charge and current excited
states of the LL. We explicitly compute the wavefunctions of these two objects
and show that one of them can be identified with the 1D version of the Laughlin
quasiparticle introduced in the context of the Fractional Quantum Hall effect.
For bosons, the other quasiparticle corresponds to a spinon excitation. The
eigenfunctions of Wen's chiral LL hamiltonian are also derived: they are quite
simply the one dimensional restrictions of the 2D bulk Laughlin wavefunctions.
