We examine and explain the Luttinger-liquid character of models solvab
le by the Bethe ansatz by introducing a suitable bosonic operator alge
bra. In the case of the Hubbard chain, this involves two bosonic algeb
ras which apply to all values of U, electronic density, and magnetizat
ion. Only at zero magnetization does this lead to the usual charge-spi
n separation. We show that our ''pseudoparticle'' operator approach cl
arifies, unifies, and extends several recent results, including the ex
istence of independent right and left equations of motion and the conc
ept of ''pseudoparticle'' (also known as ''Bethe quasiparticle'').