  We investigate the spin structure function $g_2 (x, Q^2 )$ in the framework
of the operator product expansion and the renormalization group. The twist-3
operators appearing in QCD are examined and their relations are studied. It is
noted that operators proportional to equation of motion appear in the operator
mixing through renormalization, which can be studied from the relevant Green's
functions. We also note that the coefficient functions can be properly fixed
after the choice of independent operators.
