  We show global well-posedness in energy norm of the semi-relativistic
Schr\"odinger-Poisson system of equations with attractive Coulomb interaction
in ${\mathbb R}^3$ in the presence of pseudo-relativistic diffusion. We also
discuss sufficient conditions to have well-posedness in ${\mathcal L}^2$. In
the absence of dissipation, we show that the solution corresponding to an
initial condition with negative energy blows up in finite time, which is as
expected, since the nonlinearity is critical.
