  We consider full phase-space noncommutativity in the Dirac equation, and find
that in order to preserve gauge invariance, configuration space
noncommutativity must be dropped. The resulting space structure gives rise to a
constant magnetic field background and this effect is explicitly seen on the
spectrum of the hydrogen atom. Computing this spectrum we find a bound on the
momentum noncommutative parameter $\eta$, $\sqrt{\eta}\lsim2.26\mu eV/c$.
