  We employ the Dynamical Cluster Approximation (DCA) in conjunction with the
Fluctuation Exchange Approximation (FLEX) to study the Hubbard model. The DCA
is a technique to systematically restore the momentum conservation at the
internal vertices of Feynman diagrams relinquished in the Dynamical Mean Field
Approximation (DMFA). FLEX is a perturbative diagrammatic approach in which
classes of Feynman diagrams are summed over analytically using geometric
series. The FLEX is used as a tool to investigate the complementarity of the
DCA and the finite size lattice technique with periodic boundary conditions by
comparing their results for the Hubbard model. We also study the microscopic
theory underlying the DCA in terms of compact (skeletal) and non-compact
diagrammatic contributions to the thermodynamic potential independent of a
specific model. The significant advantages of the DCA implementation in
momentum space suggests the development of the same formalism for the frequency
space. However, we show that such a formalism for the Matsubara frequencies at
finite temperatures leads to acausal results and is not viable. However, a real
frequency approach is shown to be feasible.
