  We formulate and explore the physical implications of a new translation gauge
theory of gravity in flat space-time with a new Yang-Mills action, which
involves quadratic gauge curvature and fermions. The theory shows that the
presence of an "effective Riemann metric tensor" for the motions of classical
particles and light rays is probably the manifestation of the translation gauge
symmetry. In the post-Newtonian approximation of the tensor gauge field
produced by the energy-momentum tensor, the results are shown to be consistent
with classical tests of gravity and with the quadrupole radiations of binary
pulsars.
