Abstract
A Ward identity is derived for the one-dimensional system with both electron-electron and electron-phonon forward scattering interactions. This identity is used to solve exactly the Dyson equations of the generalized effective interaction, phonon and electron Green functions for both T = 0 and T ≠ 0. The absence of both the quasi-fermion excitations and the jump in electron momentum distribution at the Fermi "surface" points out the failure of the Landau Fermi liquid theory for this system. The long-wavelength dielectric response function and the thermodynamic potential are also computed exactly.
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