Coulomb interaction and the Fermi liquid state: Solution by bosonization

We investigate the effects of the Coulomb two-body interaction on Fermi liquids via bosonization in two and three spatial dimensions. The Coulomb interaction is singular in the limit of low momentum transfer, and recent interest in the possibility that some singular interactions might destroy the Fermi liquid state motivate us to reexamine it. We calculate the exact boson correlation function to show that the Fermi liquid state is retained in the case of Coulomb interactions in two and three dimensions. Spin and charge degrees of freedom propagate together at the same velocity and collective charge excitations (plasmons) exhibit the expected energy gap in three dimensions. Non-Fermi liquid behaviour occurs in two dimensions, however, for a super-long-range interaction studied recently by Bares and Wen.