Condensed Matter Physics, 2006, vol. 9, No. 3(47), p. 499-518, English

Title: Green functions in the renormalized many-body perturbation theory for correlated and disordered electrons
  V.Janiš (Institute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, CZ-18221 Praha 8, Czech Republic)

The ways of introducing and handling renormalizations in the many-body perturbation theory are reviewed. We stress the indispensable role the technique of Green functions plays in extrapolating the weak-coupling perturbative approaches to intermediate and strong couplings. We separately discuss mass and charge renormalizations. The former is incorporated in a self-consistent equation for the self-energy derived explicitly from generating Feynman diagrams within the Baym and Kadanoff approach. The latter amounts to self-consistent equations for two-particle irreducible vertices. We analyze the charge renormalization initiated by De Dominicis and Martin and demonstrate that its realization via the parquet approach may become a powerful and viable way of using the many-body diagrammatic approach reliably in non-perturbative regimes with cooperative phenomena induced by either strong interaction or strong static randomness.

Key words: electron correlations, random potential, Green functions and many-body perturbation theory, mass and charge renormalization, parquet equations, high spatial dimensions
PACS: 05.30.Fk, 75.20.Hr, 72.15.Rn

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