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By David Pines, P. Nozieres

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L+ gflX/2). In order to restore equilibrium, the Fermi surfaces for spins + i must split, in such a way as to have the same chemical potential. L(within corrections of order x 2 ) . L. 62) By repeating the argument which led to Eq. 64) p we must pass from oiiptrto onpq • This is easily done if we assume the system to be isotropic. Mipq is then isotropic and spin antisymmetric. Making use of Eq. 65) The calculation g = 2) of ~ IS then straightforward. ~ v (0) = fl2 1 + Fo a X. 67) that the spin susceptibility IS modified by the exchange interaction Faa.

On comparing Eq. 114) ~p = ApPo(q, co). q . V p - W d€p + - We have thus obtained a formal solution for the polarization induced by the localized bare quasiparticle. We note that since the frequency w of the dressed quasiparticle is equal to q . V po' ~p depends only on ApPo(q, q . v po) ' One may show by a microscopic calculation that App,(q, w) represents the . scattering amplitude for a process in which two quasiparticles with momenta p and p' exchange momentum hq and hw. Since q and ware very small, the corresponding scattering is nearly forward.

6 Neutral Fermi Liquids amplitude (and we shall do this in the following section), such a solution is not especially helpful in obtaining an explicit expression for tp. Let us turn, therefore, to the "gross" properties of the dressed quasiparticle po, namely the total particle density PPo(q,w) and current Jpo(q, w) that it carries. Using Eq. 104), we may write PPo(q,w) = L~np(q, w) = 1 + l p JPo(q, w) = Ljp~np(q, tp, p w) = jpo p + Ljptp. 107) p The last terms on the right-hand side of these two equations correspond to the charge and current of the polarization cloud carried by the dressed quasiparticle Pv- They represent a sizable correction to the first terms, 1 andjpo' which correspond to the bare quasiparticle charge and current.

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