  We introduce the spin-operator representation for the gluon as well as quark
distribution functions as nucleon matrix element of the gauge-invariant bilocal
light-cone operators in QCD. To identify the relevant spin operators for quarks
and gluons in a unified manner, we rely on the transformation properties of the
quark and gluon fields in the coordinate space under the action of the
generator of the Lorentz group. In particular, this approach allows us to
define the transverse-spin gluon distribution function $G_T(x)$, which is the
genuine counterpart of the transverse-spin quark distribution function $g_T(x)$
relevant to the transverse-spin structure function $g_2(x, Q^2)$ in the deep
inelastic scattering. We show that $G_T(x)$ is given by the sum of the
chromoelectric and chromomagnetic correlators associated with helicity-flip by
one unit, and the treatment of the latter correlator completes the
classification of the collinear parton distribution functions up to twist
three. We show that $G_T(x)$ receives the three-gluon and quark-gluon
correlation effects and discuss the operator product expansion for $G_T(x)$. We
also discuss the relevance of the first moment of $G_T(x)$ for the partonic
decomposition of the transverse nucleon spin.
