  We investigate the nucleon's transverse spin-dependent structure function
g_2(x, Q^{2}) in the framework of the operator product expansion and the
renormalization group. We construct the complete set of the twist-3 operators
for the flavor singlet channel, and give the relations among them. We develop
an efficient, covariant approach to derive the anomalous dimension matrix of
the twist-3 singlet operators by computing the off-shell Green's functions. As
an application, we investigate the renormalization mixing for the lowest moment
case, including the operators proportional to the equations of motion as well
as the ``alien'' operators which are not gauge-invariant.
