Using a Fock-space formalism for the Master equation and introducing t
he density operator we present an unified method to derive kinetic equ
ations for hopping processes with and without exclusion on a lattice,
The corresponding Liouvillians are written in terms of Fermi or Bose o
perators, respectively. Although the Liouvillians are different the av
eraged particle numbers obey the same diffusion equation. Differences
appear in the correlation functions only. The Master equation can be t
ransformed into a differential equation in a coherent state representa
tion. Using the algebraic properties of Grassmann numbers we are able
to find the exact stationary solution for diffusion with exclusion. Th
e conductivity can be derived in the bosonic and the fermionic case. T
he results are in accordance with those obtained with different other
methods.