Abstract
An attractive d-wave interaction occurs for Cooper pairing due to magnetic fluctuations associated with both sides of the spin-density-wave phase transition, in the Hubbard model for both square and bcc lattices. This pairing interaction is not enhanced by the antiferromagnetic background that occurs in the spin-density-wave (SDW) state. The problem of magnetic Umklapp processes in the interaction for the SDW state is dealt with by using a two-component electron field to represent the two sublattices of the antiferromagnetism. A Landau-Fermi liquid is assumed for the electrons and fluctuations are treated in the random-phase approximation (RPA). We also discuss the qualitative form of the theory beyond the RPA.
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