  The momentum bands, energy dispersions, and velocities of the charge $c$
fermions and spin-neutral two-spinon $s1$ fermions of a square-lattice quantum
liquid referring to the Hubbard model on such a lattice of edge length $L$ in
the one- and two-electron subspace are studied. The model involves the
effective nearest-neighbor integral $t$ and on-site repulsion $U$ and can be
experimentally realized in systems of correlated ultra-cold fermionic atoms on
an optical lattice and thus our results are of interest for such systems. Our
investigations profit from a general rotated-electron description, which is
consistent with the model global $SO(3)\times SO(3)\times U(1)$ symmetry. For
the model in the one- and two-electron subspace the discrete momentum values of
the $c$ and $s1$ fermions are good quantum numbers so that in contrast to the
original strongly-correlated electronic problem their interactions are
residual. The use of our description renders an involved many-electron problem
into a quantum liquid with some similarities with a Fermi liquid.
