  We consider the effects of the electron-electron interaction in a clean Dirac
metal, i.e., a Dirac system with the chemical potential not tuned to the Dirac
point. We introduce the notion of a Dirac Fermi liquid (DFL) and discuss the
soft two-particle excitations in such systems, which are qualitatively
different from the corresponding excitations in a conventional, or Landau,
Fermi liquid (LFL). These soft excitations lead to nonanalytic dependencies of
observables, including the density of states, the spin susceptibility, and the
specific heat, on the temperature, magnetic field, and wave number, which first
appear at second order in the interaction. We determine and discuss the nature
of these nonanalyticities in a DFL and compare them with the corresponding
effects in a LFL. Our results are based on very general arguments regarding the
existence and nature of the soft modes, and corroborated by explicit
perturbative calculations. We also discuss their consequences for magnetic
quantum phase transitions in Dirac metals.
