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We develop a dynamical approach based on the Schwinger-Keldysh formalism toderive a field-theoretic description of disordered and interacting electronsystems. We calculate within this formalism the perturbative RG equations forinteracting electrons expanded around a diffusive Fermi liquid fixed point, asobtained originally by Finkelstein using replicas. The major simplifyingfeature of this approach, as compared to Finkelstein's is that instead of $N\to 0$ replicas, we only need to consider N=2 species. We compare the dynamicalSchwinger-Keldysh approach and the replica methods, and we present a simple andpedagogical RG procedure to obtain Finkelstein's RG equations.Comment: 22 pages, 14 figure

Schwinger-Keldysh approach to disordered and interacting electron systems: Derivation of Finkelstein’s renormalization-group equations