Quantum field theory of normal liquids

Toyoyuki Kitamura

Toyoyuki Kitamura

M. Luft, S.V. Peletminskij

David Pines

Vieri Mastropietro

In the context of the Anderson theory of high T c cuprates, we develop a BCS theory for Luttinger liquids. If the Luttinger interaction is much stronger than the BCS potential we find that the BCS equation is quite modified compared to usual BCS equation for Fermi liquids. In particular T c predicted by the BCS equation for Luttinger liquids is quite higher than the usual T c for Fermi liquids. 1 The anomalous BCS equation The equivalent of BCS theory for a Luttinger liquid has not formally worked out, despite the relevance of such theory for the problem of superconductivity in the high-T c cuprates, see [1] or the discussion in the following section. Such theory should describe superconductors which in their normal state are Luttinger liquids. In this paper we develop such theory using constructive quantum field theory techniques, applied in many other Luttinger liquid problems, see [2], [3]. In particular, we compute in a rigorous way the BCS self-consistence equation for a spinni...

Gabriele F. Giuliani, Giovanni Vignale

1. Introduction to the electron liquid 2. The Hartree-Fock approximation 3. Linear response theory 4. Linear response of independent electrons 5. Linear response of an interacting electron liquid 6. The perturbative calculation of linear response functions 7. Density functional theory 8. The normal Fermi liquid 9. The one-dimensional electron gas and the Luttinger liquid 10. The two-dimensional electron gas at high magnetic field.