  It is shown that the Sigma-Omega model which is widely used in the study of
nuclear relativistic many-body problem can exactly be treated as an Abelian
massive gauge field theory. The quantization of this theory can perfectly be
performed by means of the general methods described in the quantum gauge field
theory. Especially, the local U(1) gauge symmetry of the theory leads to a
series of Ward-Takahashi identities satisfied by Green's functions and proper
vertices. These identities form an uniquely correct basis for the
renormalization of the theory. The renormalization is carried out in the
mass-dependent momentum space subtraction scheme and by the renormalization
group approach. With the aid of the renormalization boundary conditions, the
solutions to the renormalization group equations are given in definite
expressions without any ambiguity and renormalized S-matrix elememts are
exactly formulated in forms as given in a series of tree diagrams provided that
the physical parameters are replaced by the running ones. As an illustration of
the renormalization procedure, the one-loop renormalization is concretely
carried out and the results are given in rigorous forms which are suitable in
the whole energy region. The effect of the one-loop renormalization is examined
by the two-nucleon elastic scattering.
