  The continuum Kardar-Parisi-Zhang equation in one dimension is lattice
discretized in such a way that the drift part is divergence free. This allows
to determine explicitly the stationary measures. We map the lattice KPZ
equation to a bosonic field theory which has a cubic anti-hermitian
nonlinearity. Thereby it is established that the stationary two-point function
spreads superdiffusively.
