Viewing gravitational energy-momentum as equal by observation, but different
in essence from inertial energy-momentum naturally leads to the gauge theory of
volume-preserving diffeormorphisms of an inner Minkowski space. The generalized
asymptotic free scalar, Dirac and gauge fields in that theory are canonically
quantized, the Fock spaces of stationary states are constructed and the
gravitational limit - mapping the gravitational energy-momentum onto the
inertial energy-momentum to account for their observed equality - is
introduced. Next the S-matrix in quantum gravity is defined as the
gravitational limit of the transition amplitudes of asymptotic in- to
out-states in the gauge theory of volume-preserving diffeormorphisms. The so
defined S-matrix relates in- and out-states of observable particles carrying
gravitational equal to inertial energy-momentum. Finally generalized LSZ
reduction formulae for scalar, Dirac and gauge fields are established which
allow to express S-matrix elements as the gravitational limit of truncated
Fourier-transformed vacuum expectation values of time-ordered products of field
operators of the interacting theory. Together with the generating functional of
the latter established in an earlier paper [8] any transition amplitude can in
principle be computed to any order in perturbative quantum gravity.Comment: 35 page