  We study the problem of the damping of collective modes close to a
Pomeranchuk quantum critical point in a Fermi liquid. In analogy with problems
in dissipative open quantum systems, we derive the Landau damping of a Fermi
liquid by integrating out a macroscopic number of degrees of freedom from a
generating functional. Being a reformulation of the linearized Boltzmann
equation this approach reproduces well-known results from the theory of Fermi
liquids. We also study the Bethe-Salpeter equations within the Landau theory
and discuss the implications of these results on quantum phase transitions of
the Pomeranchuk type and its dynamical exponent, z. We apply our results to the
electronic nematic instability and find z=3 in the collisionless limit.
