The Aharonov-Bohm scattering for spinless, isospin 1/2, particles interacti
ng through a non-Abelian Chern-Simons field is studied. Starring from the r
elativistic quantum field theory and using a Coulomb gauge formulation, the
one loop renormalization program is implemented. Through the introduction
of an intermediary cutoff, separating the regions of high and low integrati
on momentum, the nonrelativistic limit is derived. The next to leading rela
tivistic approximation is also determined. In this approach quantum field t
heory vacuum polarization effects are automatically incorporated. [S0556-28
21(99)04002-3].