  Viewing gravitational energy momentum $p_G^\mu$ as equal by observation, but
different in essence from inertial energy-momentum $p_I^\mu$ requires two
different symmetries to account for their independent conservations - spacetime
and inner translation invariance. Gauging the latter a generalization of
non-Abelian gauge theories of compact Lie groups is developed resulting in the
gauge theory of the non-compact group of volume-preserving diffeomorphisms of
an inner Minkowski space ${\bf M}^{\sl 4}$. As usual the gauging requires the
introduction of a covariant derivative, a gauge field and a field strength
operator. An invariant and minimal gauge field Lagrangian is derived. The
classical field dynamics and the conservation laws for the new gauge theory are
developed. Finally, the theory's Hamiltonian in the axial gauge is expressed by
two times six unconstrained independent canonical variables obeying the usual
Poisson brackets and the positivity of the Hamiltonian is related to a
condition on the support of the gauge fields.
