  The general possible form of meanfield parameterization in a running frame in
terms of current, energy and density functionals are examined under the
restrictions of Galilean invariance. It is found that only two
density-dependent parameters remain which are usually condensed in a
position-dependent effective mass and the selfenergy formed by current and
mass. The position-dependent mass induces a position-dependent local current
which is identified for different nonlinear frames. In a second step the
response to an external perturbation and relaxation towards a local equilibrium
is investigated. The response function is found to be universal in the sense
that the actual parameterization of the local equilibrium does not matter and
is eliminated from the theory due to the conservation laws. The explicit form
of the response with respect to density, momentum and energy is derived. The
compressibility sum rule as well as the sum rule by first and third-order
frequency moments are proved analytically to be fulfilled simultaneously. The
results are presented for Bose- or Fermi systems in one- two and three
dimensions.
