Abstract
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 flat physical space–time. 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.