  We introduce a new operator algebra for the description of the low-energy
physics of one-dimensional, integrable, multicomponent quantum liquids.
Considering the particular case of the Hubbard chain in a constant external
magnetic field and with varying chemical potential, we show that at low energy
its Bethe-ansatz solution can be interpreted in terms of the new {\it
pseudoparticle operator algebra}. Our algebraic approach provides a concise
interpretation of and justification for several recent studies of low-energy
excitations and transport which have been based on detailed analyses of
specific Bethe-ansatz eigenfunctions and eigenenergies. A central point is that
the {\it exact ground state} of the interacting many-electron problem is the
non-interacting pseudoparticle ground state. Furthermore, in the pseudoparticle
basis, the quantum problem becomes perturbative, {\it i.e.}, the
two-pseudoparticle forward-scattering vertices and amplitudes do not diverge,
and one can define a many-pseudoparticle perturbation theory. We write the
general quantum-liquid Hamiltonian in the new basis and show that the
pseudoparticle-perturbation theory leads, in a natural way, to the generalized
Landau-liquid approach.
