  We construct a new $U(1)$ slave spin representation for the single band
Hubbard model in the large-$U$ limit. The mean-field theory in this
representation is more amenable to describe both the spin-charge-separation
physics of the Mott insulator at half-filling and the strange metal behavior at
finite doping. By employing a dynamical Green's function theory for slave
spins, we calculate the single-particle spectral function of electrons, and the
result is comparable to that in dynamical mean field theories. We then
formulate a dynamical $t/U$ expansion for the doped Hubbard model that
reproduces the mean-field results at the lowest order of expansion. To the next
order of expansion, it naturally yields an effective low-energy theory of a
$t-J$ model for spinons self-consistently coupled to n $XXZ$ model for the
slave spins. We show that the superexchange $J$ is renormalized by doping, in
agreement with the Gutzwiller approximation. Surprisingly, we find a new
ferromagnetic channel of exchange interactions which survives in the infinite
$U$ limit, as a manifestation of the Nagaoka ferromagnetism.
