  We study the space-time structure of polynomiality and positivity---the most
important properties which are inherent to the generalized parton distributions
(GPDs). In this connection, we re-examine the issue of the time- and normal-
ordering in the operator definition of GPDs. We demonstrate that the
contribution of the anti-commutator matrix element in the collinear kinematics,
which was previously argued to vanish, has to be added in order to satisfy the
polynomiality condition. Furthermore, we schematically show that a new
contribution due to the anti-commutator modifies likewise the so-called
positivity constraint, i.e., the Cauchy-Bunyakovsky-Schwarz inequality, which
is another important feature of the GPDs.
