  Quantum periodic cluster methods for strongly correlated electron systems are
reformulated and developed. The reformulation and development are based on a
canonical transformation which periodizes the fermions in the cluster space.
The dynamical cluster approximation and the cellular dynamical mean field
theory are related each other through the canonical transformation. A cluster
perturbation theory with periodic boundary conditions is developed. It is found
that the periodic cluster perturbation theory converges rapidly with
corrections $\mathcal{O}(1/L_c^2)$, where $L_c$ is the linear size of the
clusters, whereas the ordinary cluster perturbation theory converges with
corrections $\mathcal{O}(1/L_c)$.
