  We consider the real-time evolution of the Hubbard model in the limit of
infinite coupling. In this limit the Hamiltonian of the system is mapped into a
number-conserving quadratic form of spinless fermions, i.e. the tight binding
model. The relevant local observables, however, do not transform well under
this mapping and take very complicated expressions in terms of the spinless
fermions. Here we show that for two classes of interesting observables the
quench dynamics from product states in the occupation basis can be determined
exactly in terms of correlations in the tight-binding model. In particular, we
show that the time evolution of any function of the total density of particles
is mapped directly into that of the same function of the density of spinless
fermions in the tight-binding model. Moreover, we express the two-point
functions of the spin-full fermions at any time after the quench in terms of
correlations of the tight binding model. This sum is generically very
complicated but we show that it leads to simple explicit expressions for the
time evolution of the densities of the two separate species and the
correlations between a point at the boundary and one in the bulk when evolving
from the so called generalised nested N\'eel states.
