Bosonization of Fermi liquids

Details Bosonization of Fermi liquids Bosonization of Fermi liquids

1993-07-02

arxiv.org/abs/cond-mat/9307005v1

Physics

Condensed Matter

42 pages, RevteX, preprint UIUC (1993)

Scientific paper

10.1103/PhysRevB.49.10877

We bosonize a Fermi liquid in any number of dimensions in the limit of long wavelengths. From the bosons we construct a set of coherent states which are related with the displacement of the Fermi surface due to particle-hole excitations. We show that an interacting hamiltonian in terms of the original fermions is quadratic in the bosons. We obtain a path integral representation for the generating functional which in real time, in the semiclassical limit, gives the Landau equation for sound waves and in the imaginary time gives us the correct form of the specific heat for a Fermi liquid even with the corrections due to the interactions between the fermions. We also discuss the similarities between our results and the physics of quantum crystals.

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