  Inertial and gravitational mass or energy-momentum need not be the same for
virtual quantum states. Separating their roles naturally leads to the gauge
theory of volume-preserving diffeomorphisms of an inner four-dimensional space.
The gauge-fixed action and the path integral measure occurring in the
generating functional for the quantum Green functions of the theory are shown
to obey a BRST-type symmetry. The related Zinn-Justin-type equation restricting
the corresponding quantum effective action is established. This equation limits
the infinite parts of the quantum effective action to have the same form as the
gauge-fixed Lagrangian of the theory proving its spacetime renormalizability.
The inner space integrals occurring in the quantum effective action which are
divergent due to the gauge group's infinite volume are shown to be
regularizable in a way consistent with the symmetries of the theory
demonstrating as a byproduct that viable quantum gauge field theories are not
limited to finite-dimensional compact gauge groups as is commonly assumed.
