Abstract:Année de publication : 2004
Cluster Dynamical Mean Field Theories are analyzed in terms of their semiclassical limit and their causality properties, and a translation invariant formulation of the cellular dynamical mean field theory, {\PCDMFT}, is presented. The semiclassical limit of the cluster methods is analyzed by applying them to the Falikov-Kimball model in the limit of infinite Hubbard interaction $U$ where they map to different classical cluster schemes for the Ising model. Furthermore the Cutkosky-t'Hooft-Veltman cutting equations are generalized and derived for non translation invariant systems using the Schwinger-Keldysh formalism. This provides a general setting to discuss causality properties of cluster methods. To illustrate the method, we prove that {\PCDMFT} is causal while the nested cluster schemes (NCS) in general and the pair scheme in particular are not. Constraints on further extension of these schemes are discussed.
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