  The non-equilibrium quantum field dynamics is usually described in the
closed-time-path formalism. The initial state correlations are introduced into
the generating functional by non-local source terms. We propose a functional
approach to the Dyson-Schwinger equation, which treats the non-local and local
source terms in the same way. In this approach, the generating functional is
formulated for the connected Green functions and one-particle-irreducible
vertices. The great advantages of our approach over the widely used
two-particle-irreducible method are that it is much simpler and that it is easy
to implement the procedure in a computer program to automatically generate the
Feynman diagrams for a given process. The method is then applied to a pure
gluon plasma to derive the gauge-covariant transport equation from the
Dyson-Schwinger equation in the background covariant gauge. We discuss the
structure of the kinetic equation and show its relationship with the classical
one. We derive the gauge-covariant collision part and present an approximation
in the vicinity of equilibrium. The role of the non-local source kernel in the
non-equilibrium system is discussed in the context of a free scalar field.
