The Symmetries of Fermion Fluids at Low Dimensions

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We point out that the quasiparticle spectrum of the Landau Fermi liquid theory has an extra $Z_2$ symmetry, local in momentum space, which is not generic to the Hamiltonian with interactions. Thus the Fermi liquid is in this sense a (quantum) zero-temperature critical point.
submitted to a volume honoring Quin Luttinger

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