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Single-Particle Green Functions in Exactly Solvable Models of Bose and Fermi Liquids

Based on a class of exactly solvable models of interacting bose and fermi liquids, we compute the single-particle propagators of these systems exactly for all wavelengths and energies and in any number of spatial dimensions. The field operators are expressed in terms of bose fields that correspond to displacements of the condensate in the bose case and displacements of the fermi sea in the fermi case. Unlike some of the previous attempts, the present attempt reduces the answer for the spectral function in any dimension in both fermi and bose systems to quadratures. It is shown that when only the lowest order sea-displacement terms are included, the random phase approximation in its many guises is recovered in the fermi case, and Bogoliubov's theory in the bose case. The momentum distribution is evaluated using two different approaches, exact diagonalisation and the equation of motion approach. The novelty being of course, the exact computation of single-particle properties including short wavelength behaviour.